Question

For all U.S. students nationally who take the SAT, SAT Math scores are normally distributed with an average score of 500 for all U.S. students . A random sample of 100 students entering Whitmer College had an average SAT Math (SAT-M) score of 520 and a sample standard deviation of 120. The sample data can be used to test the claim that the mean SAT-M score of all Whitmer College students is different than the national mean SAT-M score. Based on the given information, use the appropriate formula and the provided Standard Normal Table (Z table). Determine the p-value for this two-sided hypothesis test. You will need to calculate the test statistic first. Enter the p-value in the space below as a decimal rounded to four decimal places:

Answer 1

The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized mean value of 30 on either side.

Now, the value of test static can be found out by following formula:

Using Excel's function =T.DIST.2T(|t0|,n-1), the P-value for t0 = 1.6667 in an t-test with 99 degrees of freedom can be computed as

P = P(T_{99}>1.6667)=T.DIST.2T(|1.6667|,99)=0.0987

Since P = 0.0987 > 0.05, we fail to reject the null hypothesis

Since t0 = 1.6667 < -1.98 = -t{0.025}, we fail to reject the null hypothesis

We have sufficient evidence to claim that the mean SAT-M score of all Whitmer College students is different than the national mean SAT-M score