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 equals 10.1 based on earlier studies? Suppose the doctor would be content with 95 % confidence. How does the decrease in confidence affect the sample size required?

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Level of Confidence, (1minus−alphaα )times• 100%		Area in Each Tail, StartFraction alpha Over 2 EndFractionα2		Critical Value, z Subscript alpha divided by 2zα/2
90%		0.05		1.645
95%		0.025		1.96
99%		0.005		2.575

Answer 1

We have to find sample size ( n ).

Given, Margin of error = E = 3

Confidence level = 99% =0.99

significance level = = 1 - 0.99 = 0.01

standard deviation = 10.1

Formula for sample size ,

Where, is two tailed critical value .

is standard deviation.

E margin of error.

Using given table critical value for 99% confidence level is,

= = 2.575

So sample size is,

------------( 1 )

Suppose the doctor would be content with 95% confidence.

Critical value for 95% confidence level is 1.96

So sample size is,

----------------( 2)

From 1 and 2 , It is observed that if confidence level decreases then sample size also decreases.