Question

# For all U.S. students nationally who take the SAT, SAT Math scores are normally distributed with...

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:

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