Question

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

Answer 1

Calculate the mean and standard deviation of the given data. Mean (T)-2x 47508+5280265170 1757020 - 53243.03 Stadnard deviationS 2- (47508-53243.03) +..+ (65170-53243.03) 33-1 - 9445.46744305453 9445.47 (Round to 2 decimal place)

a) Null hypothesis, Ho: 50000 Alternative hypothesis, Hi:H>50000 Level of significance, α-0.05 Calculate the test statistic value. 53243.03 50000 9445.47/33 1.97 The degrees of freedom is,

33-1 - 32 Calculate the t -critical value. (aitical valueTINV(0.05,32)) (Use MS Excel function) се -1.693889 1.694 (Round to 3 decimal place) The test statistic value is greater than the t - critical value. So, we reject the null hypothesis and conclude that the there is a sufficient evidence to conclude that the average starting salary of all new commerce grads exceeds 50000 b) Calculate the P - value for the result in part (a) P -value (TDIST(1.97,32,1)) (Use MS Excel function) 0.028772 The P-value is less than the given significance level 0.05, so we reject the null hypothesis and conclude that the there is a sufficient evidence to conclude that the average starting salary of all new commerce grads exceeds 50000

c) Calculate the 95% one sided confidence interval for the average salary 95%One Sided C.1-x-r critical 9445.47 - 53243.03-1.694 N33 = 53243.03-3349.2180 - 49893.8210 49894 (Round to nearest whole number Hence, the 95% confidence that the population mean for the average salary is: 49894. d) The P value and the confidence interval calculated in the part (a) supports your conclusions that there is sufficient evidence to conclude that the population mean of the average starting salary of all new commerce graduates exceeds 50000

e) Use MS Excel to draw a Box plot: BoxPlot 20000 30000 40000 50000 60000 70000 80000 90000 100000 Data 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 outliers 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