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 higher 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 one-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

Solution :

= 520

= 520

s = 120

n = 100

This is the right tailed test .

The null and alternative hypothesis is

H0 :   = 500

Ha : > 500

Test statistic = t

= ( - ) / s / n

= (520-500) /120 / 100

= 1.667

p(t > 1.667) = 1-P (t<1.667 ) =0.0493

P-value = 0.0493