Question

A random sample of 64 second-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is 51.21. Assume the standard deviation for the population of test scores is 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second-graders in her school district have greater math skills than the nationwide average. Perform the hypothesis test and compute the p-value. Round to four decimal places.

Answer 1

This is the right tailed test .

The null and alternative hypothesis is

H₀ :   = 50

H_a : > 50

Test statistic = z

= ( - ) / / n

= (51.21 - 50) / 15 / 64

Test statistic = 0.65

P(z > 0.65) = 1 - P(z < 0.65) = 0.2578

P-value = 0.2578