Question: (20 points) A psychological test, used to measure the level of hostility, is known to produce scores which are normally distributed, with a mean of 34. Suppose that the test was administered to 25 randomly selected participants. The sample produced the mean of 39.2 and the standard deviation of 8.55. Test whether there is evidence that the mean score is significantly different from 34.

(a) State the hypotheses.

(b) Using a 5% significance level, determine the rejection and non-rejection regions.

(c) Calculate the test statistic, and interpret the result.

(d) Calculate the p-value.

(e) Calculate the 95% confidence interval for the corresponding population mean. How does this result relate to the conclusions in parts (c) and (d)?