Question: A psychological test, used to measure the level of hostility, is known to produce scores which are normally distributed, with a mean of 35. Suppose that the test was administered to 25 randomly selected individuals. The sample produced the mean of 40.2 with a standard deviation of 8.55. Test whether there is evidence that the mean score is significantly different from 35.
(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, and interpret the result.
(e) Calculate a 95% confidence interval for the corresponding population mean. How does this result relate to the conclusions in parts (c) and (d)?