Question

The College Board reported the following mean scores for three parts of the Scholastic Aptitude Test (SAT): Critical Reading 502; Mathematics 515; Writing 494. Assume that the population standard deviation on each part of the test is 100.

1. For a random sample of 64 test takers, find the standard deviation of the sampling distribution of the sample mean.

2. For a random sample of 100 test takers, find the standard deviation of the sampling distribution of the sample mean.

Answer 1

51307, Math, Statistics and Probability

Question The College Board reported the following mean scores for three parts of the Scholastic Aptitude Test (SAT): Critical Reading 502; Mathematics 515; Writing 494. Assume that the population standard deviation on each part of the test is 100. 1. For a random sample of 64 test takers, find the standard deviation of the sampling distribution of the sample mean. 2. For a random sample of 100 test takers, find the standard deviation of the sampling distribution of the sample mean.

Solution The standard deviation of the sampling distribution of a statistic is referred to as the standard error of that quantity. It can be found as

$\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$

So for 1 we have

$\sigma_{\bar{x}}=\frac{100}{\sqrt{64}}=\frac{100}{8}=12.5$

And for 2 we have

$\sigma_{\bar{x}}=\frac{100}{\sqrt{100}}=\frac{100}{10}=10$

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