1. The annual earnings of 38 people with a high school diploma and 21 people with an associate degree are shown below. Can you conclude that there is a difference in the mean annual earnings based on level of education? Assume that population are normally distributed, and population variances are not equal. High school diploma Associate degree x, = $40, 450 x, = $47, 500 S = $138 S, = $200 n = 38 n, = 21 a) What type of statistical test should be used to answer the researcher's question? (Note: Is this a z-test or a t-test? One sample, dependent sample or independent sample) (2p) b) Identify the claim and state the null and alternative hypothesis. (3p) c) Calculate the standardized test statistic and corresponding critical value(s). (5p) d) At 0.01 significance level, decide whether to reject or fail to reject the null hypothesis. (2p) e) Interpret the decision in the context of the original claim. (3p)