# Subscript

Find the critical z values. Assume that the normal distribution applies.
Two​-tailed ​test; alphaαequals=0.060.06

A random sample of 8181 eighth grade​ students’ scores on a national mathematics assessment test has a mean score of 268268 with a standard deviation of 3737. This test result prompts a state school administrator to declare that the mean score for the​ state’s eighth graders on this exam is more than 260260. At alphaαequals=0.120.12​, is there enough evidence to support the​ administrator’s claim? Complete parts​ (a) through​ (e).
​(a) Write the claim mathematically and identify Upper H 0H0 and Upper H Subscript aHa. Choose the correct answer below.
A.
Upper H 0H0​: muμless than<260 Upper H Subscript aHa​: muμgreater than or equals≥260260 ​(claim) B. Upper H 0H0​: muμless than or equals≤260260 Upper H Subscript aHa​: muμgreater than>260260 ​(claim)
C.
Upper H 0H0​: muμequals=260260
Upper H Subscript aHa​: muμgreater than>260260 ​(claim)
D.
Upper H 0H0​: muμequals=260260 ​(claim)
Upper H Subscript aHa​: muμgreater than>260260
E.
Upper H 0H0​: muμless than or equals≤260260 ​(claim)
Upper H Subscript aHa​: muμgreater than>260260

b) Find the standardized test statistic​ z, and its corresponding area.
zequals=
nothing ​(Round to two decimal places as​ needed.)
Areaequals=
nothing ​(Round to three decimal places as​ needed.)

d) Decide whether to reject or fail to reject the null hypothesis.RejectReject Upper H 0H0Fail to rejectFail to reject Upper H 0

t the 12​% significance​ level, there
is
is not
enough evidence to
support
reject
the​ administrator’s claim that the mean score for the​ state’s eighth graders on the exam is more than 260260.

At the 12​% significance​ level, there is enough evidence to support the​ administrator’s claim that the mean score for the​ state’s eighth graders on the exam is more than 260.

use the​ t-distribution table to find the critical​ value(s) for the indicated alternative​ hypotheses, level of significance alphaα​, and sample sizes n 1n1 and n 2n2. Assume that the samples are​ independent, normal, and random. Answer parts​ (a) and​ (b).
Upper H Subscript aHa​: mu 1 less than mu 2μ1<μ2​, alphaαequals=0.050.05​, n 1n1equals=1414​, n 2n2equals=1313 ​(a) Find the critical​ value(s) assuming that the population variances are equal. Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as​ needed.) ​(b) Find the critical​ value(s) assuming that the population variances are not equal.nothing ​(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as​ needed.) use the​ t-distribution table to find the critical​ value(s) for the indicated alternative​ hypotheses, level of significance alphaα​, and sample sizes n 1n1 and n 2n2. Assume that the samples are​ independent, normal, and random. Answer parts​ (a) and​ (b). Upper H Subscript aHa​: mu 1 greater than mu 2μ1>μ2​, alphaαequals=0.0250.025​, n 1n1equals=1313​, n 2n2equals=1111
​(a) Find the critical​ value(s) assuming that the population variances are equal.nothing
​(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as​ needed.)

use the given information to answer parts​ (a) through​ (d).
Upper H 0 : mu 1 equals mu 2H0: μ1=μ2​, alpha equals 0.02α=0.02
Sample​ statistics: x overbar 1 equals 36.2×1=36.2​, s 1 equals 3.7s1=3.7​, n 1 equals 15n1=15
x overbar 2 equals 35.3×2=35.3​, s 2 equals 2.8s2=2.8​, n 2 equals                           8n2=8
Assume sigma Subscript 1 Superscript 2 Baseline equals sigma Subscript 2 Superscript 2σ21=σ22.
negative t 0 equals negative 2.518−t0=−2.518​, t 0 equals 2.518t0=2.518-3
-2
-1
0
1
2
3
t
A normal curve is over a horizontal t-axis labeled from negative 3 to 3 in increments of 1 and is centered on 0. Vertical line segments extend from the horizontal axis to the curve at negative 2.518 and 2.518. The areas under the curve and to the left of negative 2.518 and to the right of 2.518 are shaded.
​(a) Find the test statistic. nothing

Recall that the test statistic is x overbar 1 minus x overbar 2×1−x2. Check your subtraction.

In over seven years of doing this, I cannot recall a single instance of the phrase “test statistic” being used this way.

Find the standardized test statistic.
Decide whether the standardized test statistic is in the rejection region.
in
not in
the rejection region.
The standardized test​ statistic, t, is in the rejection region.

Decide whether you should reject or fail to reject the null hypothesis.
use the given information to answer parts​ (a) through​ (d).
Upper H 0 : mu 1 less than or equals mu 2H0: μ1≤μ2​, alpha equals 0.10α=0.10
Sample​ statistics: x overbar 1 equals 2274×1=2274​, s 1 equals 181s1=181​, n 1 equals 6n1=6
x overbar 2 equals                           2318×2=2318​, s 2 equals 46s2=46​, n 2 equals 8n2=8
Assume sigma Subscript 1 Superscript 2 Baseline not equals sigma Subscript 2 Superscript 2σ21≠σ22.
t 0 equals 1.476t0=1.476-3
t
x y graph
​(a) Find the test statistic.
b) Find the standardized test statistic.
tequals=
nothing ​(Type an integer or decimal rounded to three decimal places as​ needed.)
The standardized test​ statistic, t, is
in
not in
the rejection region.
The standardized test​ statistic, t, is not in the rejection region.
Decide whether you should reject or fail to reject the null hypothesis.
Fail to reject
Reject
the null hypothesis.
An engineer wants to know if producing metal bars using a new experimental treatment rather than the conventional treatment makes a difference in the tensile strength of the bars​ (the ability to resist tearing when pulled​ lengthwise). At alphaαequals=0.050.05​, answer parts​ (a) through​ (e). Assume the population variances are equal and the samples are random. If​ convenient, use technology to solve the problem.
font size decreased by 1 Start 3 By 2 Table 1st Row 1st Column Treatment 2nd Column Tensile strengths left parenthesis newtons per square millimeter right parenthesis 2nd Row 1st Column Experimental 2nd Column Start 1 By 10 Matrix 1st Row 1st Column 365 2nd Column 411 3rd Column 439 4st Column 404 5st Column 380 6st Column 423 7st Column 442 8st Column 9st Column 10st Column EndMatrix 3rd Row 1st Column Conventional 2nd Column Start 1 By 10 Matrix 1st Row 1st Column 393 2nd Column 384 3rd Column 395 4st Column 395 5st Column 380 6st Column 391 7st Column 425 8st Column 433 9st Column 439 10st Column 433 EndMatrix EndTable Treatment Tensile strengths (newtons per square millimeter) Experimental 365 411 439 404 380 423 442 Conventional 393 384 395 395 380 391 425 433 439 433
​(a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa.
The claim is​ “The new treatment
makes a difference
does not make a difference
in the tensile strength of the​ bars.”
The null​ hypothesis, Upper H 0H0​, is
mu 1 equals mu 2μ1=μ2
mu 1 less than or equals mu 2μ1≤μ2
mu 1 greater than or equals mu 2μ1≥μ2
. The alternative​ hypothesis, Upper H Subscript aHa​, is
mu 1 not equals mu 2μ1≠μ2
mu 1 greater than mu 2μ1>μ2
mu 1 less than mu 2μ1<μ2 . Which hypothesis is the​ claim?The alternative​ hypothesis, Upper H Subscript aHaThe null​ hypothesis, Upper H 0 The alternative hypothesis is the claim. b) Find the critical​ value(s) and identify the rejection​ region(s). Enter the critical​ value(s) below.nothing The rejection region is the graph with both tails shaded. Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as​ needed.) Select the correct rejection​ region(s) below. A. t greater than t 0t>t0
B.
t less than minus t 0 comma t greater than t 0t<−t0, t>t0
C.
t less than minus t 0t<−t0
D.
negative t 0 less than t less than t 0
Find the standardized test statistic.
tequals=
nothing
​(Type an integer or decimal rounded to the nearest thousandth as​ needed.)
Decide whether to reject or fail to reject the null hypothesis.
Fail to reject
Reject
the null hypothesis.
Fail to reject
Interpret the decision in the context of the original claim.
At the 5 %5% significance​ level,
there is not
there is
enough evidence to support the claim
At the 5% significance​ level, there is not enough evidence to support the claim.

use technology to help test the claim about the difference between two population means mu 1μ1 and mu 2μ2 at the given level of significance alphaα using the given sample statistics. Assume that the population is normally​ distributed, and the samples are independent and random. Assume sigma Subscript 1 Superscript 2 Baseline equals sigma Subscript 2 Superscript 2σ21=σ22.
​Claim:
mu 1 less than or equals mu 2μ1≤μ2​; alphaαequals=0.100.10
Sample​ statistics:
x overbar 1x1equals=181181​, s 1s1equals=3838​, n 1n1equals=1414 and x overbar 2x2equals=193193​, s 2s2equals=4343​, n 2n2equals=99
Identify the null and alternative hypotheses. Choose the correct answer below.
A.
Upper H 0H0​: mu 1μ1minus−mu 2μ2greater than or equals≥0
Upper H Subscript aHa​: mu 1μ1minus−mu 2μ2less than<0
B.
Upper H 0H0​: mu 1μ1minus−mu 2μ2less than<0 Upper H Subscript aHa​: mu 1μ1minus−mu 2μ2equals=0 C. Upper H 0H0​: mu 1μ1minus−mu 2μ2equals=0 Upper H Subscript aHa​: mu 1μ1minus−mu 2μ2not equals≠0 D. Upper H 0H0​: mu 1μ1minus−mu 2μ2less than or equals≤0 Upper H Subscript aHa​: mu 1μ1minus−mu 2μ2greater than>
Find the standardized test statistic.
tequals=
nothing ​(Round to three decimal places as​ needed
Check that you have used the technology correctly. Note that the formula of the standardized test statistic for a​ two-sample t-test for the difference between means when the variances are equal is as shown below.
tequals=StartFraction left parenthesis x overbar 1 minus x overbar 2 right parenthesis minus left parenthesis mu 1 minus mu 2 right parenthesis Over s Subscript x overbar 1 minus x overbar 2 EndFraction
x1−x2−μ1−μ2
sx1−x2
The pooled estimate of the standard deviation is ModifyingAbove sigma with caretσ.
ModifyingAbove sigma with caretσequals=StartRoot StartFraction left parenthesis n 1 minus 1 right parenthesis s Subscript 1 Superscript 2 Baseline plus left parenthesis n 2 minus 1 right parenthesis s Subscript 2 Superscript 2 Over n 1 plus n 2 minus 2 EndFraction EndRoot
n1−1s21+n2−1s22
n1+n2−2
The standard error for the sampling distribution of x overbar 1x1minus−x overbar 2×2 is s Subscript x overbar 1 minus x overbar 2sx1−x2​, and d.f.equals=n 1n1plus+n 2n2minus−2.
s Subscript x overbar 1 minus x overbar 2sx1−x2equals=ModifyingAbove sigma with caret times StartRoot StartFraction 1 Over n 1 EndFraction plus StartFraction 1 Over n 2 EndFraction EndRoot
29-Jul-17
calculate the​ P-value.
Pequals=
nothing ​(Round to four decimal places as​ needed.)
tate the conclusion. Fill in the blanks below.
Fail to reject
Reject
Upper H 0H0. There
is
is not
enough evidence at the 1010​% level of significance to reject the claim
Fail to reject H0. There is not enough evidence at the 10​% level of significance to reject the claim.
What conditions are necessary in order to use the dependent samples t​-test for the mean of the difference of two​ populations?
A.
Each sample must be randomly selected from any population and each member of the first sample must be paired with a member of the second sample.
B.
Each sample must be randomly selected from any population and the two samples must be independent.
C.
Each sample must be randomly selected from a normal population and the two samples must be independent.
D.
The table below shows the critical reading scores for 14 students the first two times they took a standardized test. At alphaαequals=​0.01, is there enough evidence to conclude that their scores improved the second time they took the​ test? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (f).
Student
​(a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa.
The claim is​ “The students’ critical reading test scores
improved
did not change
decreased
changed
the second time they took the​ test.”
The claim is​ “The students’ critical reading test scores improved the second time they took the​ test.”

Let mu Subscript dμd be the hypothesized mean of the the​ students’ first score minus their second score. State Upper H 0H0 and Upper H Subscript aHa. Choose the correct answer below.
A.
Upper H 0H0​: mu Subscript dμdless than or equals≤0
Upper H Subscript aHa​: mu Subscript dμdgreater than>0
B.
Upper H 0H0​: mu Subscript dμdnot equals≠0
Upper H Subscript aHa​: mu Subscript dμdequals=0
C.
Upper H 0H0​: mu Subscript dμdequals=0
Upper H Subscript aHa​: mu Subscript dμdnot equals≠0
D.
Upper H 0H0​: mu Subscript dμdgreater than or equals≥d overbard
Upper H Subscript aHa​: mu Subscript dμdless thand overbard
F.
Upper H 0H0​: mu Subscript dμdgreater than or equals≥0
Upper H Subscript aHa​: mu Subscript dμd

Find the critical​ value(s) and identify the rejection​ region(s).
t 0t0equals=
​(use a comma to separate answers as needed. Type an integer or a decimal. Round to three decimal places as​ needed

Identify the rejection​ region(s). Choose the correct answer below.
A.
tless than<minus−2.650 B. tgreater than>3.012
C.
tless than<minus−3.012 or tgreater than>3.012
D.
tless than<minus−2.650 or tgreater than>2.650

Calculate d overbard and s Subscript dsd.
d overbardequals=
nothing
​(Type an integer or a decimal. Round to three decimal places as​ needed.)
use the​ t-test to find the standardized test statistic t.
tequals=
nothing
​(Type an integer or a decimal. Round to three decimal places as​ needed.)
Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.RejectReject the null hypothesis.Fail to rejectFail to reject the null hypothesis.

Interpret the decision in the context of the original claim. Choose the correct answer below.
A.
At the​ 1% significance​ level, there isis enough evidence that the​ students’ critical reading scores improved the second time they took the test.
B.
At the​ 1% significance​ level, there is evidence that the​ students’ critical reading scores got worse the second time they took the test.
C.
D.
The sample was not large enough to make a conclusion.
The table below shows the gas mileages​ (in miles per​ gallon) of eight cars with and without using a fuel additive. At alphaαequals=​0.10, is there enough evidence to conclude that the fuel additive improved gas​ mileage? Complete parts​ (a) through​ (f).
Car
23.323.3
27.127.1
25.025.0
26.626.6
20.720.7
24.324.3
21.821.8
23.023.0
​(a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa.
The claim is​ “The fuel additive
did not change
changed
improved
decreased
gas​ mileage.”
Let mu Subscript dμd be the hypothesized mean of the the​ cars’ gas mileage without additive minus their gas mileage with additive. State Upper H 0H0 and Upper H Subscript aHa. Choose the correct answer below.
A.
Upper H 0H0​: mu Subscript dμdnot equals≠0
Upper H Subscript aHa​: mu Subscript dμdequals=0
B.
Upper H 0H0​: mu Subscript dμdequals=0
Upper H Subscript aHa​: mu Subscript dμdnot equals≠0
C.
Upper H 0H0​: mu Subscript dμdless than or equals≤d overbard
Upper H Subscript aHa​: mu Subscript dμdgreater than>d overbard
D.
Upper H 0H0​: mu Subscript dμdgreater than or equals≥d overbard
Upper H Subscript aHa​: mu Subscript dμdless than E.
Upper H 0H0​: mu Subscript dμdgreater than or equals≥0
Upper H Subscript aHa​: mu Subscript dμdless than<0 F. Upper H 0H0​: mu Subscript dμdless than or equals≤0 Upper H Subscript aHa​: mu Subscript dμdgreater than>0
Find the critical​ value(s) and identify the rejection​ region(s).
t 0t0equals=
nothing
​(use a comma to separate answers as needed. Type an integer or a decimal. Round to three decimal places as​ needed.)
Identify the rejection​ region(s). Choose the correct answer below.
A.
tgreater than>1.895
B.
tless than<minus−1.415
C.
tless than<minus−1.415 or tgreater than>1.415
D.
tless than<minus−1.895 or tgreater than>1.895

Calculate d overbard and s Subscript dsd.
d overbardequals=
nothing
​(Type an integer or a decimal. Round to three decimal places as​ needed

use the​ t-test to find the standardized test statistic t.
tequals=
nothing
​(Type an integer or a decimal. Round to three decimal places as​ needed
RejectReject the null hypothesis.Fail to rejectFail to reject the null hypothesis.
f) Interpret the decision in the context of the original claim. Choose the correct answer below.
A.
At the​ 10% significance​ level, there isis enough evidence that the fuel additive improved gas mileage.
B.
At the​ 10% significance​ level, there is notis not enough evidence that the fuel additive improved gas mileage.
C.
At the​ 10% significance​ level, there is enough evidence that the gas mileage was worse when using the fuel additive.
D.
The sample was not large enough to make a conclusion.

What conditions are necessary in order to use the z​-test to test the difference between two population​ proportions?
A.
Each sample must be randomly​ selected, independent, and n 1 p 1 comman1p1, n 1 q 1 comman1q1, n 2 p 2 comman2p2, and n 2 q 2n2q2 must be at most five.
B.
Each sample must be randomly​ selected, independent, and n 1 p 1 comman1p1, n 1 q 1 comman1q1, n 2 p 2 comman2p2, and n 2 q 2n2q2 must be at least five.
C.
Each sample must be randomly​ selected, dependent, and n 1 p 1 comman1p1, n 1 q 1 comman1q1, n 2 p 2 comman2p2, and n 2 q 2n2q2 must be at most five.
D.
Each sample must be randomly​ selected, dependent, and n 1 p 1 comman1p1, n 1 q 1 comman1q1, n 2 p 2 comman2p2, and n 2 q 2n2q2 must be at least five.

Test the following claim about the difference between two population proportions p 1p1 and p 2p2 for the given level of significance alphaα and the given sample statistics. Is the test​ right-tailed, left-tailed, or​ two-tailed? Assume the sample statistics are from independent random samples.
p 1p1not equals≠p 2p2​, ​Claim:  alphaαequals=0.100.10
x 1x1equals=2121​, n Sample​ statistics:  1n1equals=9696 and x 2x2equals=3636​, n 2n2equals=6363
Is the test​ right-tailed, left-tailed, or​ two-tailed?​Right-tailed​Left-tailed​Two-tailed
two-tailed
Should the null hypothesis be​ rejected?
A.
RejectReject Upper H 0H0. There is sufficientsufficient evidence to support the claim.
B.
RejectReject Upper H 0H0. There is insufficientinsufficient evidence to support the claim.
C.
Fail to rejectFail to reject Upper H 0H0. There is insufficientinsufficient evidence to support the claim.
D.
Fail to rejectFail to reject Upper H 0H0. There is sufficientsufficient evidence to support the claim.
A. Reject H0. There is sufficient evidence to support the claim.
Decide whether the normal sampling distribution can be used. If it can be​ used, test the claim about the difference between two population proportions p 1p1 and p 2p2 at the given level of significance alphaα using the given sample statistics. Assume the sample statistics are from independent random samples.
​Claim:
p 1p1equals=p 2p2​, alphaαequals=0.010.01
Sample​ statistics:
x 1x1equals=5858​, n 1n1equals=168168 and x 2x2equals=2424​, n 2n2equals=193193
Can a normal sampling distribution be​ used?No

Identify the null and alternative hypotheses. Choose the correct answer below.
A.
Upper H 0H0​: p 1p1equals=p 2p2
Upper H Subscript aHa​: p 1p1not equals≠p 2p2
B.
Upper H 0H0​: p 1p1less than

p 2p2
E.
A normal sampling distribution cannot be​ used, so the claim cannot be tested
Find the critical values. Select the correct choice below​ and, if​ necessary, fill in the answer boxes to complete your choice.
A.
The critical values are minus−z 0z0equals=
nothing  and  z 0z0equals=
nothing.
​(Round to two decimal places as​ needed.)
B.
A normal sampling distribution cannot be​ used, so the claim cannot be tested.
Find the standardized test statistic. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
zequals=
nothing ​(Round to two decimal places as​ needed.)
B.
A normal sampling distribution cannot be​ used, so the claim cannot be tested.
z = 5.00

State the conclusion. Choose the correct answer below.
A.
RejectReject Upper H 0H0. There is insufficientinsufficient evidence that there is a difference between p 1p1 and p 2p2.
B.
Fail to rejectFail to reject Upper H 0H0. There is insufficientinsufficient evidence that there is a difference between p 1p1 and p 2p2.
C.
RejectReject Upper H 0H0. There is sufficientsufficient evidence that there is a difference between p 1p1 and p 2p2.
D.
Fail to rejectFail to reject Upper H 0H0. There is sufficientsufficient evidence that there is a difference between p 1p1 and p 2p2.
E.
A normal sampling distribution cannot be​ used, so the claim cannot be tested.

Test the following claim about the difference between two population proportions p 1p1 and p 2p2 for the given level of significance alphaα and the given sample statistics. Is the test​ right-tailed, left-tailed, or​ two-tailed? Assume the sample statistics are from independent random samples.
p 1p1less than or equals≤p ​Claim:  2p2​, alphaαequals=0.100.10
x 1x1equals=562562​, n Sample​  1n1equals=988988 and x 2x2equals=316316​, n 2n2equals=771771 statistics:
Is the test​ right-tailed, left-tailed, or​ two-tailed?LeftLeft​-tailed​Two-tailedRightRight​-tailed

Should the null hypothesis be​ rejected?
A.
RejectReject Upper H 0H0. There is insufficientinsufficient evidence to reject the claim in support of p 1p1greater than>p 2p2.
B.
RejectReject Upper H 0H0. There is sufficientsufficient evidence to reject the claim in support of p 1p1greater than>p 2p2.
C.
Fail to rejectFail to reject Upper H 0H0. There is sufficientsufficient evidence to reject the claim in support of p 1p1greater than>p 2p2.
D.
Fail to rejectFail to reject Upper H 0H0. There is insufficientinsufficient evidence to reject the claim in support of p 1p1greater than>p 2p2.
B. Reject H0. There is sufficient evidence to reject the claim in support of p1 > p2.

In a study of 18871887 ​adults, 596596 said they has used alternative medicines in the previous year. In a more recent study of 28332833 ​adults, 918918 said they had used alternative medicines in the previous year. At alphaαequals=0.100.10​, can you reject the claim that the proportion of adults using alternative medicines has not changed since the first​ study? Assume the random samples are independent. Complete parts​ (a) through​ (e).
​(a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa.
The claim is​ “the proportion of adults using alternative medicines has

decreased
increased
changed
not changed
since the first​ study.”
The claim is​ “the proportion of adults using alternative medicines has not changed since the first​ study.”

Let p 1p1 and p 2p2 be the two population proportions. State Upper H 0H0 and Upper H Subscript aHa.
A.
Upper H 0H0​: p 1p1greater than>p 2p2
Upper H Subscript aHa​: p 1p1less than or equals≤p 2p2
B.
Upper H 0H0​: p 1p1greater than or equals≥p 2p2
Upper H Subscript aHa​: p 1p1less than

p 2p2
D.
Upper H 0H0​: p 1p1equals=p 2p2
Upper H Subscript aHa​: p 1p1not equals≠p 2p2
E.
Upper H 0H0​: p 1p1not equals≠p 2p2
Upper H Subscript aHa​: p 1p1equals=p 2p2
F.
Upper H 0H0​: p 1p1less than

Upper H Subscript aHa​: p 1p1greater than or equals≥p 2

Find the critical​ value(s) and identify the rejection​ region(s).
z 0z0equals=
nothing
​(Use a comma to separate answers as needed. Type an integer or a decimal. Round to threethree decimal places as​ needed.)
Identify the rejection​ region(s). Choose the correct answer below.
Find the standardized test statistic.
zequals=
nothing ​(Round to two decimal places as​ needed.)
Decide whether to reject or fail to reject the null hypothesis.
Choose the correct answer below.RejectReject Upper H 0H0.Fail to rejectFail to reject Upper H 0H0.
e) Interpret the decision in the context of the original claim.
A.
At the 1010​% significance​ level, there is sufficientsufficient evidence to support the claim.
B.
At the 1010​% significance​ level, there is insufficientinsufficient evidence to support the claim.
C.
At the 1010​% significance​ level, there is sufficientsufficient evidence to reject the claim.
D.
At the 1010​% significance​ level, there is insufficientinsufficient evidence to reject the claim.
.
In a survey of 54455445 male senior​ citizens, 18161816 said they eat the daily recommended number of servings of vegetables. In a survey of 59025902 female senior​ citizens, 19851985 said they eat the daily recommended number of servings of vegetables. At alphaαequals=0.100.10​, can you reject the claim that the proportions of senior citizens who said they eat the daily recommended number of servings of vegetables are the same for the two​ groups? Assume the random samples are independent. Complete parts​ (a) through​ (e).
​(a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa.
The claim is​ “the proportion of male senior citizens who said they eat the daily recommended number of servings of vegetables is
different than
less than
the same as
greater than
the proportion of female senior citizens who said they eat the daily recommended number of servings of​ vegetables”
The claim is​ “the proportion of male senior citizens who said they eat the daily recommended number of servings of vegetables is

the proportion of female senior citizens who said they eat the daily recommended number of servings of​ vegetables”
Let p 1p1 and p 2p2 be the two population proportions. State Upper H 0H0 and Upper H Subscript aHa.
A.
Upper H 0H0​: p 1p1less than

p 2p2
C.
Upper H 0H0​: p 1p1greater than or equals≥p 2p2
Upper H Subscript aHa​: p 1p1less than

p 2p2
Upper H Subscript aHa​: p 1p1less than or equals≤p 2p2
E.
Upper H 0H0​: p 1p1equals=p 2p2
Upper H Subscript aHa​: p 1p1not equals≠p 2p2
F.
Upper H 0H0​: p 1p1not equals≠p 2p2
Upper H Subscript aHa​: p 1p1equals=p 2
Find the critical​ value(s) and identify the rejection​ region(s).
z 0z0equals=
nothing
​(use a comma to separate answers as needed. Type an integer or a decimal. Round to threethree decimal places as​ needed
Identify the rejection​ region(s). Choose the correct answer below.
A.
zless than<minus−1.6451.645​, zgreater than>1.6451.645
B.
zless than<minus−1.281.28​, zgreater than>1.281.28
C.
zless than<minus−1.6451.645 D. zgreater than>1.28

Find the standardized test statistic.
zequals=
nothing ​(Round to two decimal places as​ needed.

Decide whether to reject or fail to reject the null hypothesis.
Choose the correct answer below.RejectReject Upper H 0H0.Fail to rejectFail to reject Upper H 0H0.

e) Interpret the decision in the context of the original claim.
A.
At the 1010​% significance​ level, there is sufficientsufficient evidence to reject the claim.
B.
At the 1010​% significance​ level, there is insufficientinsufficient evidence to support the claim.
C.
At the 1010​% significance​ level, there is sufficientsufficient evidence to support the claim.
D.
At the 10​% significance​ level, there is insufficientinsufficient evidence to re

In a survey of 12061206 adult​ males, 820820 said they use the Internet. In a survey of 19751975 females 14881488 said they use the Internet. At alphaαequals=0.100.10​, can you reject the claim that the proportions of Internet users are the same for the two​ groups? Assume the random samples are independent. Complete parts​ (a) through​ (e).
​(a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa.
The claim is​ “the proportion of adult male Internet users is
the same as
less than
greater than
different than
the proportion of female Internet​ users.”
The claim is​ “the proportion of adult male Internet users is

the proportion of female Internet​ users.”

Let p 1p1 and p 2p2 be the two population proportions. State Upper H 0H0 and Upper H Subscript aHa.
A.
Upper H 0H0​: p 1p1not equals≠p 2p2
Upper H Subscript aHa​: p 1p1equals=p 2p2
B.
Upper H 0H0​: p 1p1less than or equals≤p 2p2
Upper H Subscript aHa​: p 1p1greater than>p 2p2
C.
Upper H 0H0​: p 1p1greater than or equals≥p 2p2
Upper H Subscript aHa​: p 1p1less than

p 2p2
Upper H Subscript aHa​: p 1p1less than or equals≤p 2p2
E.
Upper H 0H0​: p 1p1less than

1.281.28
B.
zless than<minus−1.281.28​, zgreater than>1.281.28
C.
zless than<minus−1.6451.645​, zgreater than>1.6451.645
D.
zless than<minus−1.645
Find the standardized test statistic.
zequals=
nothing ​(Round to two decimal places as​ needed.)
Choose the correct answer below.RejectReject Upper H 0H0.Fail to rejectFail to reject Upper H 0H0.

e) Interpret the decision in the context of the original claim.
A.
At the 1010​% significance​ level, there is sufficientsufficient evidence to reject the claim.
B.
At the 1010​% significance​ level, there is insufficientinsufficient evidence to support the claim.
C.
At the 1010​% significance​ level, there is insufficientinsufficient evidence to reject the claim.
D.
At the 1010​% significance​ level, there is sufficientsufficient evidence to support the claim.

A. At the 10​% significance​ level, there is sufficient evidence to reject the claim.

use the given information to answer parts​ (a) through​ (d).
Upper H 0 : mu 1 equals mu 2H0: μ1=μ2​, alpha equals 0.10α=0.10
Sample​ statistics: x overbar 1 equals 33.5×1=33.5​, s 1 equals 3.7s1=3.7​, n 1 equals 14n1=14
x overbar 2 equals 34.4×2=34.4​, s 2 equals 2.3s2=2.3​, n 2 equals                           13n2=13
Assume sigma Subscript 1 Superscript 2 Baseline equals sigma Subscript 2 Superscript 2σ21=σ22.
negative t 0 equals negative 1.708−t0=−1.708​, t 0 equals 1.708

use the given information to answer parts​ (a) through​ (d).
Upper H 0 : mu 1 equals mu 2H0: μ1=μ2​, alpha equals 0.10α=0.10
Sample​ statistics: x overbar 1 equals 33.5×1=33.5​, s 1 equals 3.7s1=3.7​, n 1 equals 14n1=14
x overbar 2 equals 34.4×2=34.4​, s 2 equals 2.3s2=2.3​, n 2 equals                           13n2=13

A normal curve is over a horizontal t-axis labeled from negative 3 to 3 in increments of 1 and is centered on 0. Vertical line segments extend from the horizontal axis to the curve at negative 1.708 and 1.708. The areas under the curve and to the left of negative 1.708 and to the right of 1.708 are shaded.
​(a) Find the test statistic.
Find the standardized test statistic.
tequals=
nothing ​(Type an integer or decimal rounded to three decimal places as​ needed.)
use a​ two-sample t-test for the difference between means when the variances are equal.
t equals StartFraction left parenthesis x overbar 1 minus x overbar 2 right parenthesis minus left parenthesis mu 1 minus mu 2 right parenthesis Over sigma Subscript x overbar 1 minus x overbar 2 EndFractiont=
x1−x2−μ1−μ2
σx1−x2
The pooled estimate of the standard deviation is ModifyingAbove sigma with caretσ.
ModifyingAbove sigma with caret equals StartRoot StartFraction left parenthesis n 1 minus 1 right parenthesis s Subscript 1 Superscript 2 Baseline plus left parenthesis n 2 minus 1 right parenthesis s Subscript 2 Superscript 2 Over n 1 plus n 2 minus 2 EndFraction EndRootσ=
n1−1s21+n2−1s22
n1+n2−2
The standard error for the sampling distribution of x overbar 1 minus x overbar 2×1−x2 is sigma Subscript x overbar Sub Subscript font size decreased by 1 1 Subscript minus x overbar Sub Subscript font size decreased by 1 2σx1−x2.
sigma Subscript x overbar Sub Subscript font size decreased by 1 1 Subscript minus x overbar Sub Subscript font size decreased by 1 2 Baseline equals ModifyingAbove sigma with caret times StartRoot StartFraction 1 Over n 1 EndFraction plus StartFraction 1 Over n 2 EndFraction EndRootσx1−x2=σ•
1
n1+
1
n2
OK
Decide whether the standardized test statistic is in the rejection region.
The standardized test​ statistic, t, is
in
not in
the rejection region.
The standardized test​ statistic, t, is
the rejection region.
Decide whether you should reject or fail to reject the null hypothesis.
Fail to reject
Reject
the null hypothesis.

Find the critical​ value(s) for the indicated​ t-test, level of significance alphaα​, and sample size n.
LeftLeft​-tailed ​test, alphaαequals=0.0250.025​, nequals=1717
The critical​ value(s) is/are
nothing.
​(Round to the nearest thousandth as needed. Use a comma to separate answers as​ needed.)

An infinite number line, labeled from 0.15 to 0.21, has tick marks in increments of 1. The region between an open circle at 0.155 and an open circle at 0.175 is shaded and labeled 0.155<p<0.175.
0.15
0.16
0.17
0.18
0.19
0.2
0.21
0.155 less than p less than 0.1750.155<p<0.175
​(a) Choose the correct answer below.
A.
RejectReject H0. The confidence interval includes values less thanincludes values less than 0.180.18.
B.
Fail to rejectFail to reject H0. The confidence interval includes values less thanincludes values less than 0.180.18.
C.
Fail to rejectFail to reject H0. The confidence interval includes values greater thanincludes values greater than 0.180.18.
D.
RejectReject H0. The confidence interval includes values greater thanincludes values greater than 0.180.18.

The three confidence intervals to the right represent three samplings. Decide whether each confidence interval indicates that you should reject H0. Explain your reasoning.
An infinite number line, labeled from 0.51 to 0.57, has tick marks in increments of 1. The region to the left of a closed circle at 0.54 is shaded and labeled H@Sub{0}:p≤0.54.
0.51
0.52
Upper H 0 : p less than or equals 0.54H0: p≤0.54
left parenthesis a right parenthesis(a)
An infinite number line, labeled from 0.51 to 0.57, has tick marks in increments of 1. The region between an open circle at 0.55 and an open circle at 0.56 is shaded and labeled 0.55<p<0.56.
0.57
0.53 less than p less than 0.550.53<p<0.55
left parenthesis b right parenthesis(b)
An infinite number line, labeled from 0.51 to 0.57, has tick marks in increments of 1. The region between an open circle at 0.55 and an open circle at 0.56 is shaded and labeled 0.55<p<0.56.
0.57
0.55 less than p less than 0.560.55<p<0.56
left parenthesis c right parenthesis(c)
An infinite number line, labeled from 0.51 to 0.57, has tick marks in increments of 1. The region between an open circle at 0.535 and an open circle at 0.565 is shaded and labeled 0.535<p<0.565.
0.535 less than p less than 0.5650.535<p<0.565
​(a) Choose the correct answer below.
A.
Fail to rejectFail to reject H0. The confidence interval includes values less thanincludes values less than 0.540.54.
B.
Fail to rejectFail to reject H0. The confidence interval includes values greater thanincludes values greater than 0.540.54.
C.
RejectReject H0. The confidence interval includes values less thanincludes values less than 0.540.54.
D.
RejectReject H0. The confidence interval includes values greater thanincludes values greater than 0.540.54.

H0. The confidence interval is located to the right ofis located to the right of 0.540.54.
B.
Fail to rejectFail to reject H0. The confidence interval is located to the right ofis located to the right of 0.540.54.
C.
RejectReject H0. The confidence interval includes values less thanincludes values less than 0.540.54.
D.
Fail to rejectFail to reject H0. The confidence interval includes values less thanincludes values less than 0.540.54
A.
Reject Reject H0. The confidence interval includes values less than includes values less than 0.540.54.
B.
Reject Reject H0. The confidence interval includes values greater than includes values greater than 0.540.54.
C.
Fail to rejectFail to reject H0. The confidence interval includes values less thanincludes values less than 0.540.54.
D.
Fail to reject Fail to reject H0. The confidence interval includes values greater than includes values greater than 0.540.54.

An automotive manufacturer claims the mean price of a small SUV isis ​\$26 comma 54526,545. If a hypothesis test is​ performed, how should you interpret a decision that​ (a) rejects the null hypothesis and​ (b) fails to reject the null​ hypothesis?
​(a) Choose the correct answer below.
A.
There is enough evidence to support the claim that the mean price of a small SUV isis ​\$26 comma 54526,545.
B.
There is not enough evidence to reject the claim that the mean price of a small SUV isis ​\$26 comma 54526,545.
C.
There is enough evidence to reject the claim that the mean price of a small SUV isis ​\$26 comma 54526,545.
D.
There is not enough evidence to support the claim that the mean price of a small SUV isis ​\$26 comma 54526,545.

b) Choose the correct answer below.
A.
There is not enough evidence to support the claim that the mean price of a small SUV isis ​\$26 comma 54526,545.
B.
There is enough evidence to reject the claim that the mean price of a small SUV isis ​\$26 comma 54526,545.
C.
There is enough evidence to support the claim that the mean price of a small SUV isis ​\$26 comma 54526,545.
D.
There is not enough evidence to reject the claim that the mean price of a small SUV isis ​\$26 comma 54526,545