Question: Suppose a group of high school students (n = 500) take a standardized test and have a mean score \(\bar{X}\) = 461. The population mean and standard deviation for this test are \(\mu \) = 450 and \(\sigma \) = 100. The research is interested in testing the research hypothesis that this sample of students come from a higher scoring population.

a. State the null and alternative hypotheses for this problem.

b. Calculate the appropriate test statistic.

c. Determine the p-value of the test statistic, z-critical value, x critical value

d. Summarize your conclusion from these results. (use a Type I error=0.05)