Question

1) Someone you know claims that the average earnings of all waiters in the United States is $3/hour. Let Y be a random variable (i.i.d.) equal to the hourly earnings of a waiter in the U.S. You wish to gather evidence (collect a sample of data) and test the null hypothesis that the average hourly earnings of all waiters in the United States (Uy) is equal to $3 against the two-sided alternative hypothesis that it is not equal to $3. Suppose you collect a sample of 900 U.S. waiters, and find that the average earnings of the waiters in your sample is equal to $4 while the standard deviation of earnings in your sample is $50. Finally, suppose that the maximum probability of a Type 1 error that you are willing to tolerate is 5%. nalysis of Economic Data (Summer 2020) uiz #4 tatistics (a) State the null and alternative hypotheses (.5 points) (b) Calculate that t-statistic (.5 points) (c) Calculate the p-value (.5 points) (d) Compute the 95% confidence interval for My (1 point) (e) Based on either the p-value or the t-statistic, do you reject or fail to reject the null hypothesis? For full credit explain how you arrived to this conclusion. You cannot simply state “Reject” or “Fail to Reject.” You need to explain why you are taking the

Answer 1

VS ta Ans (al The hull and alternative hypotheses are Ho: My = 3 Ha! My & 3 (two-sided) (61 The test statistic in ta X-My t-distribution with (n-1) sin degrees of freedom Given that for n=goo , X= 4 s=50 SO 4 - 3 = 30 = 0.6 50/900 50 P-value =2p(1>0,6) ; Int(899) & 0:0.05 = 2x0,274329 = 0.54 0657 (d) The 95% confidence interval for My in S Vn = (4 + 3.271) = (0.729,7.271) (c) The p-value is tein-1)=1.9626 for d20.05, h=899

(C) Since p-value is greater than 0=0.05, so eve nego do not reject Ho. We conclude that there is insufficient date to support the alternative hypotheses that average hourly earnings of all waiters in us is not equal to $3,