3. A report states that the mean yearly salary offer for students graduating with a degree in accounting is $48,722. Suppose that a random sample of 45 accounting graduates at a large university who received job offers resulted in a mean offer of $49,870 and a standard deviation of $3900. Test at the 5% level of significance if the sample data provide strong support for the claim that the mean salary offer for accounting graduates of this university is statistically higher than the national average of $48,722?
(a) Identify the correct null ($H_0$) and alternative ($H_a$) hypotheses.
i. $\mu = 48,722$, $\mu \ne 48,722$
ii. $\mu = 48,722$, $\mu < 48,722$
iii. $\mu = 48,722$, $\mu > 48,722$
(b) Find the test statistic value.
(c) Find the critical value using the traditional method.
(d) Based on your answers above, you
i. Fail to reject the $H_0$.
ii. Reject the $H_0$.
(e) Explain your choice for part (d).
(f) Based on your work above, choose one of the following conclusions of your test.
i. There is sufficient evidence to warrant rejection of the claim.
ii. There is not sufficient evidence to support the claim.
iii. The sample data supports the claim.
iv. There is not sufficient evidence to warrant rejection of the claim.
g) Explain your choice for part (f).