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 2 points with 99 % confidence assuming s equals 19.1 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
nothing subjects. ​(Round up to the nearest​ subject.)

Answer 1

Answer:

Explanation:

99% confidence:

For 99% confidence interval, α=1-0.99=0.01

α/2=0.01/2=0.005

z(0.005)=2.576

Margin of error:

MoE= z(0.005)*s/sqrt(n)

MoE=2.576*19.1/ sqrt(n)

MoE=2

So, 2.576 *19.1/sqrt(n)

n=605.2

Sample size=605

90% confidence:

For 90% confidence interval, α=1-0.9=0.1

α/2=0.1/2=0.05

Z(0.05)=1.645

MoE:

MoE= Z(0.05)*S/sqrt(n)

MoE=1.645*19.1/sqrt(n)

MoE=2

So, 1.645*19.1/sqrt(n)=2

n=246.7

Sample size =247

So, decreasing the confidence level decreases the sample size

Answer 2

Answer:

confidence coefficient for 99% is 2.58

2.58 * 19.4/sqrt(n) = 0.04

2.598*19.4/0.04 = sqrt(n)

( 2.598*19.4/0.04)^2  = n

1587676

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confidence coefficient for 90% is 1.64

(1.64*19.4/0.04)^2 = 632661.16