A doctor wants to estimate the HDL cholesterol of all 20- to 29-year old females

Question

A doctor wants to estimate the HDL cholesterol of all 20- to 29-year old females. Hon 99% confidence assuming o-199? Suppose old females. How many subjects are needed to estimate the HDL cholesterol within 3 points wh 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 whole number as needed ) 6667% A 90% confidence level requires subjects (Round up to the nearest whole number as needed ) How does the decrease in confidence affect the sample size required? O A. The lower the confidence level the larger the sample size O B. The sample size is the same for all levels of confidence C. The lower the confidence level te smaller the sample size Click to select your answers) e to search

Explanation / Answer

a) Step 1: Find z a/2 by dividing the confidence interval by two, and looking that area up in the z-table:

.99/2 = 0.495. The closest z-score for 0.495 is 2.58.

Step 2: Multiply step 1 by the standard deviation.
2.58 * 19.9 = 51.342

Step 3: Divide Step 2 by the margin of error. Our margin of error (from the question), is 3.
51.342/3 = 17.114

Step 4: Square Step 3.
17.114 * 17.114 = 292.88

sample size = 293 subjects

b) Step 1: Find z a/2 by dividing the confidence interval by two, and looking that area up in the z-table:

.90/2 = 0.45. The closest z-score for 0.455 is 1.645

Step 2: Multiply step 1 by the standard deviation.
1.645 * 19.9 = 32.7355

Step 3: Divide Step 2 by the margin of error. Our margin of error (from the question), is 3
32.7355/3= 10.911

Step 4: Square Step 3.
10.911*10.911 = 119.06

sample size = 119

The lower the confidence level the smaller the sample size. option c

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