# According ​research

According to a​ research, 52.052.0​% of households nationwide used natural gas for heating during a year.​ Recently, a survey of 2 comma 3002,300 randomly selected households showed that 53.053.0​% used natural gas. use a 0.05 significance level to test the claim that the 52.052.0​% national rate has changed.
Formulate the null and alternative hypotheses. Choose the correct answer below.
A.
Upper H 0H0​: pnot equals≠0.520.52​, Upper H Subscript aHa​: pequals=0.520.52
B.
Upper H 0H0​: pgreater than>0.520.52​, Upper H Subscript aHa​: pless than<0.520.52 C. Upper H 0H0​: pequals=0.520.52​, Upper H Subscript aHa​: pgreater than>0.520.52
D.
Upper H 0H0​: pequals=0.520.52​, Upper H Subscript aHa​: pnot equals≠0.520.52

Find the test statistic.
zequals=
nothing ​(Round to one decimal place as​ needed.)
Find the​ P-value for the found test statistic.
​P-valueequals=
nothing ​(Round to four decimal places as​ needed.)
Now make a conclusion. Choose the correct answer below.
A.
There is not enough information to make a conclusion.
B.
There is not sufficient evidence to support the claim that the percentage of households using natural gas has changed.
C.
There is sufficient evidence to support the claim that the percentage of households using natural gas has changed

IQ scores are normally distributed with a mean of 105 and a standard deviation of 15. Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample.
a. If the sample size is n equals=64​, find the mean and standard deviation of the distribution of sample means.
The mean of the distribution of sample means is——
The standard deviation of the distribution of sample means is
——–.
​(Type an integer or decimal rounded to the nearest tenth as​ needed.)
b. If the sample size is nequals=144144​, find the mean and standard deviation of the distribution of sample means.
The mean of the distribution of sample means is
——
The standard deviation of the distribution of sample means is
​(Type an integer or decimal rounded to the nearest tenth as​ needed.)
mean = 105
sd = 1.875 or rounded off to 1.9

b. If the sample size is n =144

mean = 105

sd = 1.25 or rounded off to 1.3

Why is the standard deviation in part a different from the standard deviation in part​ b? Choose the correct answer below.
A.
With smaller sample sizes​ (as in part​ a), the means tend to be further​ apart, so they have more​ variation, which results in a smaller standard deviation.
B.
With larger sample sizes​ (as in part​ b), the means tend to be closer​ together, so they have less​ variation, which results in a smaller standard deviation.
C.
With smaller sample sizes​ (as in part​ a), the means tend to be closer​ together, so they have less​ variation, which results in a smaller standard deviation.
D.
With larger sample sizes​ (as in part​ b), the means tend to be further​ apart, so they have more​ variation, which results in a bigger standard deviation

The mean birth weight of male babies born to 121 mothers taking a vitamin supplement is 3.643.64 kilograms with a standard deviation of 0.610.61 kilogram. Use a 0.05 significance level to test the claim that the mean birth weight of all babies born to mothers taking the vitamin supplement is equal to 3.39 kilograms, which is the mean for the population of all male babies.
State the null and alternative hypotheses. Choose the correct answer below.
A.
Upper H 0H0: muμequals=3.39 kg, Upper H Subscript aHa: muμnot equals≠3.39 kg
B.
Upper H 0H0: muμnot equals≠3.39 kg, Upper H Subscript aHa: muμless than<3.39 kg C. Upper H 0H0: muμnot equals≠3.39 kg, Upper H Subscript aHa: muμgreater than>3.39 kg
D.
Upper H 0H0: muμequals=3.39 kg, Upper H Subscript aHa: muμless than<3.39 kg
Make a conclusion. Choose the correct answer below.
A.
There is sufficient evidence to support the claim that the mean birth weight of male babies born to mothers on a vitamin supplement is different from the national average for all male babies.
B
There is not sufficient evidence to support the claim that the mean birth weight of male babies born to mothers on a vitamin supplement is different from the national average for all male babies.
In a Gallup poll of 1,082 randomly selected American sportsmen, 89% said that cloning of humans should not be allowed.
Identify the sample, population, and sampling method. Then comment on whether you think it is likely that the sample is representative of the population.
Identify the sample. Choose the correct answer below.
A.
the 1,082 randomly selected American sportsmen
B.
sportsmen of the whole world
C.
89% of randomly selected American sportsmen
D.
all American sportsmen
Identify the population. Choose the correct answer below.
A.
89% of randomly selected American sportsmen
B.
the 1,082 randomly selected American sportsmen
C.
sportsmen of the whole world
D.
all American sportsmen
Identify the sampling method. Choose the correct answer below.
A.
Random
B.
Systematic
C.
Convenience
Comment on whether you think it is likely that the sample is representative of the population.
A.
The members of the sample have different characteristics than members of the population, so the sample is not likely to be representative of the population.
B.
The size of the sample is not equal to the size of the population, so the sample is likely to be representative of the population.

A study was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases have a distribution that appears to be approximately bell-shaped with a mean of \$9,007 and a standard deviation of \$5,629. Use the t distribution to construct the confidence interval estimate of the population mean.
Find the 95% confidence interval.\$
The members of the sample have different characteristics than members of the​ population, so the sample is not likely to be representative of the population.
B.
The size of the sample is not equal to the size of the​ population, so the sample is likely to be representative of the population.
C.
The sample is fairly large and random. Assuming it was obtained by a reputable​ firm, the sample is likely to be representative of the population.

The lengths of the first 10 words of 2 books are listed below. Find the range and standard deviation for each of the two samples, then compare the two sets of results. Does there appear to be a difference in variation?
Book 1 : 6 2 4 3 5 2 3 5 4 5
Book 2 : 4 12 4 3 10 3 1 10 12 2
Find the range for book 1.
Range =——– letters
Find the range for book 2.
Range =——– lettersFind the standard deviation for book 1.
Sample standard deviation =———-
letters
(Do not round until the final answer. Then round to one decimal place as needed.)
Find the standard deviation for book 2.
Sample standard deviation=———
nothing letters
(Do not round until the final answer. Then round to one decimal place as needed.)

Is there a difference in variation between the two books?
A.
Yes, there is much less variation among the word lengths in book 2book 2.
B.
No, there is not a difference in the variation.
C.
Yes, there is much less variation among the word lengths in book 1book 1.
A nine-year-old tested professional touch therapists. Using a cardboard partition, she held a hand above one of the therapist’s hands, and the therapist was asked to identify the hand that was chosen.
What type of study is this? What are the variables of interest?
A.
Experiment. The variable of interest is the result of either correct or incorrect for each trial.
B.
Experiment. The variable of interest is which hand is chosen by the therapist for each trial.
C.
Observational study. The variable of interest is the result of either correct or incorrect for each trial.
D.
Observational study. The variable of interest is which hand is chosen by the therapist for each trial.

Based on data from a college, scores on a certain test are normally distributed with a mean of 1530 and a standard deviation of 322.
LOADING… Click the icon to view the table with standard scores and percentiles for a normal distribution.
a. Find the percentage of scores greater than 2013.———% (Round to two decimal places as needed.)
b. Find the percentage of scores less than 886.——-% (Round to two decimal places as needed.)
c. Find the percentage of scores between 1208 and 1852.——-% (Round to two decimal places as needed.)
Standard score Percent
-3 0.13
-2.5 0.62
-2 2.28
-1.5 6.68
-1 15.87
-0.9 18.41
3.5 99.98
use this table for above Q
a. Find the percentage of scores greater than 2013.
b. Find the percentage of scores less than 886.

c. Find the percentage of scores between 1208 and 1852.

One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.24 hour is desired. Past studies suggest that a population standard deviation of 1.2 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
The required sample size is —–.
(Round up to the nearest whole​ number.)
Based on a recent survey of adults in 60,000 households, a labor department reported an unemployment rate of 4.5%. The margin of error was 0.2 percentage point.
a. Based on the given information, state what you think was the goal of the study. Identify a possible population and the population parameter of interest.
What is the goal of this study? Choose the correct answer below.
A.
To determine the percentage of adults who are unemployed
B.
To determine if adults can be unemployed and keep their households
C.
To determine how many adults in each household are unemployed
D.
To determine what effect unemployment has on household status

Identify a possible population. Choose the correct answer below.
A.
The complete set of all unemployed adults
B.
4.5% of adults of the 60,000 households selected for the survey
C.
The complete set of all adults
D.
The complete set of all employed adults
Identify the population parameter of interest. Choose the correct answer below.
A.
The total number of all adults
B.
The margin of error
C.
The percentage of adults of the 60,000 households selected for the survey who are unemployed
D.
The percentage of all adults who are unemployed
b. Briefly describe the sample, raw data, and sample statistic for the study.

What is the sample for this study? Choose the correct answer below.
A.
The sample of adults selected for the survey
B.
C.
The complete set of all adults
D.
4.5% of the adults selected for the survey

Briefly describe the raw data for the study. Choose the correct answer below.
A.
The percentage of adults of the 60,000 households selected for the survey who are unemployed
B.
The 95% confidence interval
C.
The percentage of all adults who are unemployed
D.
Individual responses to the question

Briefly describe the sample statistic for the study. Choose the correct answer below.
A.
4.5%
B.
60,000 households selected for the survey
C.
The number of all adults who are unemployed
D.
0.2 percentage points
c. Based on the sample statistic and the margin of error, identify the range of values likely to contain the population parameter of interest.

Identify the type I error and the type II error that corresponds to the given hypothesis.
The proportion of settled medical malpractice suits is 0.34.
Which of the following is a type I error?
A.
Fail to reject the claim that the proportion of settled malpractice suits is 0.34 when the proportion is actually 0.34.
B.
Fail to reject the claim that the proportion of settled malpractice suits is 0.34 when the proportion is actually different from 0.34.
C.
Reject the claim that the proportion of settled malpractice suits is 0.34 when the proportion is actually 0.34.
D.
Reject the claim that the proportion of settled malpractice suits is 0.34 when the proportion is actually different from 0.34.

Which of the following is a type II error?
A.
Fail to reject the claim that the proportion of settled malpractice suits is 0.34 when the proportion is actually different from0.34.
B.
Reject the claim that the proportion of settled malpractice suits is 0.34 when the proportion is actually 0.34.
C.
Reject the claim that the proportion of settled malpractice suits is 0.34 when the proportion is actually different from 0.34.
D.
Fail to reject the claim that the proportion of settled malpractice suits is 0.34 when the proportion is actually 0.34.
A study was conducted of pleas made by 1,030 criminals. Among those criminals, 957 pled guilty, and 399 of them were sentenced to prison. Among the 73 other criminals, who pled not guilty, 53 were sent to prison. Complete (a) through (d).
a. What percentage of the criminals pled guilty?

b. What percentage of the criminals were sent to prison?

c. Among those who pled guilty, what is the percentage who were sent to prison?

d. Among those who pled not guilty, what is the percentage who were sent to prison?

Each car in a sample of seven cars was tested for nitrogen oxide emissions (in grams per mil and the following were obtained
0.07 0.11 0.19 0.15 0.14 0.08 0.15
Assuming that this sample is representative of cars in use construct a 95% C I of the mean amount of nitrogen oxide emissions of all cars

Workers and senior-level bosses were asked if it was seriously unethical to monitor employee e-mail. The results are summarized in the table to the right. Use a 0.05 significance level to test the claim that the response is independent of whether the subject is a worker or a boss.
Yes
No
Workers
193- yes
244- no
Bosses
38- yes
86- no
a. State the null and the alternative hypotheses. Choose the correct answer below.
A.
The null hypothesis: There is some relationship between response and whether the subject is a worker or a senior-level boss.
The alternative hypothesis: Response is independent of whether the subject is a worker or a senior-level boss.
B.
The null hypothesis: Response is independent of whether the subject is a worker or a senior-level boss.
The alternative hypothesis: There is some relationship between response and whether the subject is a worker or a senior-level boss.

using the given significance​ level, complete the test of the claim that the two variables are independent. State the conclusion that addresses the original claim. Choose the correct answer below.
There does appear to be a relationship between improvement and treatment​ (drug or​ placebo).

Each car in a sample of seven cars was tested for​ nitrogen-oxide emissions​ (in grams per​ mile), and the following results were obtained.
0.07​, 0.12​, 0.0.17​, 0.16​, 0.15​, 0.07​, 0.16
a. Assuming that this sample is representative of cars in​ use, construct a​ 95% confidence interval estimate of the mean amount of​ nitrogen-oxide emissions for all cars.nothingless than<muμless than<
nothing
​(Round to the nearest thousandth as​ needed.)

One agency requires that​ nitrogen-oxide emissions be less than 0.177 ​gram/ mile. Someone claims that​ nitrogen-oxide emissions have a mean equal to 0.177 ​gram/mile. Does the confidence interval suggest that this claim is not​ valid?YesNo