The National Center for Educational Statistics (NCES) reports that the average score for 12th graders who took the national reading test was 295 (on a scale of 1 to 500) (source: nces.ed.gov). A random sample of 100 12 th graders in Blanchet County, Alabama, schools recently took the test. Students in the sample had an average score of 301. Given the following hypotheses, H0: μ = 295 (The mean score for the population of Blanchet 12 th graders is the same as the national average.) Ha: μ ≠ 295 (The mean score for the population of Blanchet 12 th graders is not the same as the national average.)
a. Compute the p value for the sample result in this two tailed test. Assume the population standard deviation is 38 points.
b. Should you reject the null hypothesis at the 5% significance level? Explain.