Question

Question 7: A government report on remuneration for university administrators in Canada lists average salaries for various executive roles. The total annual salary for university presidents is listed as $500,000. To test this reported figure, at LOC = 95%, a random sample of 16 Canadian university presidents’ total annual salaries was collected. The raw data is below (in $/year): 618,000, 464,000, 686,000, 500,000, 746,000, 704,000, 596,000, 629,000, 523,000, 756,000, 561,000, 608,000, 691,000, 663,000, 529,000, 442,000. a) Assess the government report’s claim, using the critical-value method. b) Use the p-value method to determine if there are any commonly-used LOC values for which the conclusion would be opposite to your answer from Part (a).

Answer 1

Sample = { 618000, 464000, 686000, 500000, 746000, 704000, 596000, 629000, 523000, 756000, 561000, 608000, 691000, 663000, 529000, 442000 }

Sample size, n= 16

Sample mean, = 607250

Sample standard deviation, s = 97457.341

a) Null and Alternative Hypotheses

Critical value:

At =0.05 and df= 16-1=15, and the critical value for a two-tailed test is t_c = 2.131

Test Statistics:

Decision about the null hypothesis:

It is observed that t = 4.402 > t_c = 2.131, it is then concluded that the null hypothesis is rejected.

b) Using p-value method:

p-value is p = 0.0005

No, there are no commonly-used LOC values for which the conclusion would be opposite to your answer from Part (a). because for that the 1-LOC value has to be less than 0.0005, which is not commoly used.