Question

​Level of​ Confidence,

​(1−α​)•​100%

90%

Area in Each​ Tail, a/2

0.05

Critical​ Value, z α/2

1.645

​95%

0.025

1.96

​99%

0.005

2.575

A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 3 points with 99 % confidence assuming s=10.2 based on earlier​ studies? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size​ required?

A​ 99% confidence level requires ______subjects. ​(Round up to the nearest​ subject.)

A 90 % confidence level requires______subjects. ​(Round up to the nearest​ subject.)

How does the decrease in confidence affect the sample size​ required? Please pick which one below:

A. Decreasing the confidence level decreases the sample size needed.

B. Decreasing the confidence level increases the sample size needed.

C. The sample size is the same for all levels of confidence.

Answer 1

a)

Confidence level = 0.99

Zc = 2.575   ( Using z table)

Margin of error = E = 3

Population standard deviation = = 10.2

We have to find sample size (n)

A​ 99% confidence level requires 77 subjects.

b)

Confidence level = 0.90

Zc = 1.645 ( Using z table)

Margin of error = E = 3

Population standard deviation = = 10.2

We have to find sample size (n)

A​ 90% confidence level requires 32 subjects.

c)

A. Decreasing the confidence level decreases the sample size needed.