Question

On average, students with a major from the Walton College of Business (WCOB) take 4 months to find a job after graduation. The Dean has suggested that the WCOB may be able to decrease the mean time that it takes graduates to find jobs by placing more students in internships. Therefore, the WCOB partnered with a number of local and national businesses to place undergraduates in internships that are relevant to their majors. A sample of 25 members of the first class to be involved in this program took an average of 3.25 months to find a job with a standard deviation of 2.0 months. What would be the correct critical value of the test statistic if you wanted to test the hypotheses at the 0.10 significance level?

t = 1.711

t = -1.711

t = 1.318

t = -1.318

Answer 1

t = -1.318

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 4
Alternative Hypothesis: μ < 4

Rejection Region
This is left tailed test, for α = 0.1 and df = 24
Critical value of t is -1.318.
Hence reject H0 if t < -1.318

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (3.25 - 4)/(2/sqrt(25))
t = -1.875

P-value Approach
P-value = 0.037
As P-value < 0.1, reject the null hypothesis.