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The file salaries.mtw contains the starting salaries of a sample of new commerce graduates. (a) Test...

The file salaries.mtw contains the starting salaries of a sample of new commerce graduates.
(a) Test at the 0.05 level of significance whether there is sufficient evidence to conclude that the average starting salary of all new commerce grads exceeds $50,000. Use the critical value approach and show manually how the t-statistic is calculated.

(b) Now show how you would calculate the p-value for the result in part (a).

(c) Calculate manually a 95% 1-sided confidence interval for the average salary.

(d) Explain why the p-value and confidence interval do or do not support your conclusion in part (a).

(e) Show a boxplot of the data and explain whether the assumptions of the test and confidence interval are reasonable.

salary
47508
52802
54906
62425
44996
41279
54308
56199
74659
53188
58387
62125
56557
44685
30962
53814
64389
57446
57694
51371
52474
47797
51889
45710
46557
52960
70545
50568
34922
64528
40670
53530
65170


math   Statistics-And-Probability   
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Answer #1

(a) To perform this right-tail hypothesis test, we use the six-step method. Step1: The null and altemative hypotheses are as follows Ho 50000 (The populati on mean is equal to 50000) versus H: Step2: We have selected a sample of 33. We decide to use a 0.05 Step3: Because ơ is unknown, you use the t-distribution and the t-test statistic We must assume that the population mean are normally distributed. Step4: For a given sample size, n, the test stati stic t foll ows a t distribution with n-1 degrees of freedom. The critical values of the t di stribution with 33-1-32 degrees of freedom 50000 (The population mean is greater than 50000) The table of t test is obtained by using the excel function -tinv(probabihty, degrees of freedom) tin(0.05,32) 1.693889 0532 1.693889 Step5: The sample mean is X 53243 he standard deviation is s= 9445 The sample Size 1sn 33 The formula for calculating the t-test statistic is given by 53243-50000 9445 133 3243 9445 5.744563 3243 1644.163 1.972432 t 19724 (b) Step6: The P-value approach P-value- P(t>1.9724) 1-P(t < 1.9724) 10.971373 0.028627 P-alue 0028627a005. We reject the null hypothesis Ho Step7: Decision Since, the test stati sti c is H1.9724t0.05,32 1.693889. We reject the null hypothesis Ho There is sufficient evidence to reject the null hypothesis Ho Hence, we conclude that the population mean of the average starting sal ary of all new commerce graduates exceeds $50,000

(d) The P-value and the confidence interval calculatedin the part(a) supports your conclusi on that there is sufficient evi dence to conclude that the populati on mean of the average starting salary of all new commerce graduates exceeds $50,000 (e) The step-by-step instructions to obtain a boxplot output using Minitab 18 software: *Store the variable X in the Minitab 18 worksheet * Choose the Graph → Boxplot-> Simple Select the variable X in the Graph vaiable boxt el ect the variable *Click ok The boxplot of Minitab 18:

Boxplot of salary Boxplot of salary 80000 70000 60000 50000 40000 30000

Interpretation:

The box plot of salary indicates that the distribution is approximately normally distributed. Since, the mean is greater than that of the median of salaries. There exists outlier in the data. The assumption of the t-test conducted and the confidence intervals calculated in the parts (a) and (c) yields the conclusions are reasonable.

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