Question

Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys 42 entry level mechanical engineers and 58entry level electrical engineers. Their mean salaries were $46,300 and $46,800, respectively. Their standard deviations were $3440 and $4220, respectively. Conduct a hypothesis test at the 5% level to determine if you agree that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary. Let the subscript m = mechanical and e = electrical.

NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

a.) State the distribution to use for the test. (Enter your answer in the form z or t_df where df is the degrees of freedom. Round your answer to two decimal places.)

Answer 1

Let be the true mean entry level mechanical engineering salary and be the true mean entry level electrical engineering salary. We need to do a hypothesis test at the 5% level to determine if you agree that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.

a) The sample sizes are greater than 30 for each of the samples and these samples are independent. This is an independent sample test for difference in the means and we will use normal distribution to test the hypotheses. That is we will use a z-test.

the hypotheses are

We have the following information from the sample

The standard deviation of the 2 populations are not known. We will estimate them using the sample

The estimated standard error of the difference between the means is

The hypothesized value of the difference in true mean salary is

The test statistics is

This is a left tailed test (The alternative hypothesis has "<")

The left tail critical value for alpha=0.05 is

Using the standard normal tables we get for z=1.645, P(Z<1.645) = 0.945

The left tail critical value is -1.645

We will reject the null hypothesis if the test statistics is less than the critical value.

Here, the test statistics is -0.65 and it is not less than the critical value -1.645. Hence we do not reject the null hypothesis.

We conclude that, at 5% level of significance, there is no sufficient evidence to support the claim that that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.

In other words, if we cannot agree that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.