Question

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Suppose you take a sample of 36 engineering majors and find their average starting salary is $60,000. The population standard deviation for starting salary for engineers is known to be 6,000. Suppose you want to test for whether the true starting salary is different than 62,500.

a. What is the null and alternative hypotheses for this test? (5 POINTS)

b. What are the critical values for conducting the hypothesis test at the 10%, 5%, and 1% significance levels? (5 POINTS)

c. What is the test statistic for the above hypothesis test, and what is the p-value? (5 POINTS)

d. At what significance levels out of 10, 5 and 1% could you reject the null hypothesis, and why? (5 POINTS)

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 62500
Alternative Hypothesis, Ha: μ ≠ 62500

b)

Rejection Region
This is two tailed test, for α = 0.1
Critical value of z are -1.645 and 1.645.
Hence reject H0 if z < -1.645 or z > 1.645

Critical value of z are -1.96 and 1.96.

Critical value of z are -2.576 and 2.576.

c)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (60000 - 62500)/(6000/sqrt(36))
z = -2.5

P-value Approach
P-value = 0.0124

d)

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

As P-value < 0.05, reject the null hypothesis.

As P-value > 0.01, fail to reject the null hypothesis.