# HDL

A doctor wants to estimate the HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 4 points with 99% confidence assuming σ=11.7? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size​ required?

use the confidence interval to find the estimated margin of error. Then find the sample mean.
A biologist reports a confidence interval of left parenthesis (2.1,2.9) when estimating the mean height​ (in centimeters) of a sample of seedlings.
Find the critical value z Subscript czc necessary to form a confidence interval at the level of confidence shown below.

Match the level of​ confidence, cequals=0.950.95​, with its representation on the number​ line, given x overbar equals 56.7x=56.7​, sequals=8.88.8​, and nequals=9090.
Choose the correct number line below.
A.
53
54
55
56
57
58
59
60
61
54.2
59.2
x overbar equals 56.7x=56.7
B.
53
54
55
56
57
58
59
60
61
54.9
58.5
x overbar equals 56.7x=56.7
C.
53
54
55
56
57
58
59
60
61
54.5
58.9
x overbar equals 56.7x=56.7
D.
53
54
55
56
57
58
59
60
61
55.2
58.2
x overbar equals 56.7x=56.7

The confidence interval is (54.88, 58.52), so it appears that choice B is what they are looking for.
Homework: Homework 3 (Read 5.1 to 5.4 and 6.1 to 6.3) Save
Score: 0 of 1 pt 49 of 81 (71 complete)
HW Score: 84.25%, 84.25 of 100 pts

Construct the confidence interval for the population mean muμ.
cequals=0.980.98​, x overbar equals 4.9x=4.9​, sequals=0.30.3​, and nequals=4848
A 9898​% confidence interval for muμ is left parenthesis nothing comma nothing right parenthesis .

Find the minimum sample size n needed to estimate muμ for the given values of​ c, s, and E.
cequals=0.980.98​, sequals=8.18.1​, and Eequals=22
Assume that a preliminary sample has at least 30 members.
nequals=

You are given the sample mean and the sample standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals.
A random sample of 6060 home theater systems has a mean price of ​\$119.00119.00 and a standard deviation is ​\$15.3015.30.
Construct a​ 90% confidence interval for the population mean.
The​ 90% confidence interval is left parenthesis nothing comma nothing right parenthesis
.In a survey of 10201020 ​adults, 803803 disapprove of the job the legislature is doing.
Use technology to construct​ 90%, 95%, and​ 99% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.
A​ 90% confidence interval for the population proportion is left parenthesis nothing comma nothing right parenthesis

In a survey of 10271027 ​adults, 805805 disapprove of the job the legislature is doing.
Use technology to construct​ 90%, 95%, and​ 99% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.
A​ 90% confidence interval for the population proportion is left parenthesis nothing comma nothing right parenthesis.In a survey of 10271027 ​adults, 805805 disapprove of the job the legislature is doing.
Use technology to construct​ 90%, 95%, and​ 99% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.
A​ 90% confidence interval for the population proportion is left parenthesis nothing comma nothing right parenthesis

In a survey of 10271027 ​adults, 805805 disapprove of the job the legislature is doing.
Use technology to construct​ 90%, 95%, and​ 99% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.
A​ 90% confidence interval for the population proportion is left parenthesis nothing comma nothing right parenthesis

A beverage company uses a machine to fill​ one-liter bottles with water​ (see figure). Assume that the population of volumes is normally distributed.
​(a) The company wants to estimate the mean volume of water the machine is putting in the bottles within 1 milliliter. Determine the minimum sample size required to construct a 9090​% confidence interval for the population mean. Assume the population standard deviation is 55 milliliters.
​(b) Repeat part​ (a) using an error tolerance of 22 milliliters. Which error tolerance requires a larger sample​ size? Explain.

If a random variable x is normally​ distributed, you can find the probability that x will fall in a given interval by calculating the area under the normal curve for the given interval. To find the area under the normal​ curve, first convert the upper bound of the interval to a​ z-score. Use either technology or the standard normal table to find the area corresponding to the​ z-score. To convert the area to a percent multiply by 100.
Use the normal distribution of SAT critical reading scores for which the mean is 510510 and the standard deviation is 114114. Assume the variable x is normally distributed.
left parenthesis a right parenthesis(a)
What percent of the SAT verbal scores are less than 550550​?
left parenthesis b right parenthesis(b)
If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than 525525​?
left parenthesis a right parenthesis(a) Approximately
nothing​% of the SAT verbal scores are less than 550550.
​(Round to two decimal places as​ needed.)

A doctor wants to estimate the HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 44 points with 99 %99% confidence assuming sigma equals 13.7 question mark σ=13.7? Suppose the doctor would be content with 90 %90% confidence. How does the decrease in confidence affect the sample size​ required?