Question

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=18.1

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.)

90%confidence level requires ____ subjects. ​(Round up to the nearest​ subject.)

Answer 1

Solution :

1) Sample size required at 99% confidence level is given as follows :

Where, Z(0.01/2) is critical z-value at 99% confidence level, is estimated value of population standard deviation and E is margin of error.

Since, we need to estimate the mean HDL cholesterol within 3 points, therefore E = 3

Using Z-table we get, Z(0.01/2) = 2.576

Hence, required sample size is,

On rounding to nearest integer we get,

n = 242.

Hence, a 99% confidence level requires 242 subjects.

2) Sample size required at 90% confidence level is given as follows :

Where, Z(0.10/2) is critical z-value at 90% confidence level, is estimated value of population standard deviation and E is margin of error.

Since, we need to estimate the mean HDL cholesterol within 3 points, therefore E = 3

Using Z-table we get, Z(0.10/2) = 1.645

Hence, required sample size is,

On rounding to nearest integer we get,

n = 98

Hence, a 90% confidence level requires 98 subjects.