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 475 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 lower 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:

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 500

Ha: 500

The test statistics,

z =( - )/ (/n)

= ( 475 - 500 ) / ( 120 / 100 )

= -2.083

P-value = P(Z < z )

= P(Z < -2.083 )

= 0.0186