Question

A large university is well known for both its law school and its nursing program. The dean of the career services office wants to know if there is a difference in starting job salary between recently graduated law majors and nursing majors. The starting annual salaries for a random sample of 30 law majors and 30 nursing majors from the most recent graduating class are taken. Assume that the population standard deviation of the law majors' starting salaries is $12,000 and the population standard deviation of the nursing majors' starting salaries is $7,000, and that the starting salaries for both majors are normally distributed. Let the law majors' salaries be the first sample, and let the nursing majors' salaries be the second sample. The dean conducts a two-mean hypothesis test at the 0.05 level of significance, to test if there is evidence of a difference in average annual starting salary. H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.

"Law Majors"   Nursing Majors
72000   73000
66000   60000
78000   67000
46000   80000
72000   64000
54000   67000
68000   62000
33000   55000
73000   79000
59000   72000
59000   72000
62000   63000
71000   65000
47000   69000
41000   70000
67000   68000
49000   54000
59000   67000
54000   68000
90000   69000
39000   75000
88000   71000
61000   77000
59000   50000
69000   79000
62000   68000
66000   62000
63000   74000
69000   78000
42000   75000

The above table shows the starting annual salaries for a random sample of 30 law majors and 30 nursing majors from the most recent graduating class. Use Excel to test if the mean annual starting salaries are the same for both majors. Identify the test statistic, z, and p-value from the Excel output. Round your test statistic to two decimal places and your p-value to three decimal places.

Provide your answer below: test statistic = , p-value =

Answer 1

The sample means are shown below:

Also, the provided population standard deviations are:

σ1​=12000, σ2​=7000

and the sample sizes are n1​=30 and n2​=30.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:μ1​=μ2​

Ha:μ1​ μ2​

This corresponds to a two-tailed test, for which a z-test for two population means, with known population standard deviations will be used.

(2) Rejection Region

The significance level is α=0.05, and the critical value for a two-tailed test is zc​=1.96.

The rejection region for this two-tailed test is R = { z : ∣z∣ > 1.96}

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that |∣z∣ = 2.826 > zc ​= 1.96, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0047, and since p = 0.0047 < 0.05, it is concluded that the null hypothesis is rejected.

Yes, there is sufficient evidence to claim that there is a difference in the average annual starting salary of law majors and nursing majors.