Question

Assume that the sample is a simple random sample obtained from a normally distributed population of IQ scores of statistics professors. Use the table below to find the minimum sample size needed to be 99​% confident that the sample standard deviation s is within 1​% of sigma. Is this sample size​ practical?

sigma To be​ 95% confident that s is within ​1% ​5% ​10% ​20% ​30% ​40% ​50%

of the value of sigma​, the sample size n should be at least ​19,205 768 192 48 21 12 8

To be​ 99% confident that s is within ​1% ​5% ​10% ​20% ​30% ​40% ​50%

of the value of sigma​, the sample size n should be at least ​33,218 ​1,336 336 85 38 22 14

The minimum sample size needed is ____.

Is this sample size​ practical?

A. Yes​, because the sample size is small enough to be practical for most applications.

B. ​No, because the sample size should be as small as possible for most applications.

C. No​, because the sample size is excessively large to be practical for most applications.

D. ​Yes, because the sample size should be as large as possible for most applications.

Answer 1

Given Table:

To be 95 % confident that s is within:        1 %       5 %     10 %     20 % 30 %   40 %      50 % of the value of , the sample size n should be 19,205        768         192     48      21       12            8

To be 99 % confident that s is within:                 1%       5%     10 %   20 % 30 %    40 %      50 % of the value of , the sample size n should be 33,218 1,336    336     85       38         22           14

Here

Confidence level = 99 %

Sample standard deviation s within 1 % of :

From the above Table:

The minimum sample size needed is 33,218

The correct option:

No, because the sample size is excessively large to be practicle for most applications.

C. No,