Chapter 10: Q. 81 (page 601)

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 $50$ entry level mechanical engineers and $60$ entry level electrical engineers. Their mean salaries were $\$46,100$ and $\$46,700$, respectively. Their standard deviations were $\$3,450$ and $\$4,210$, respectively. Conduct a hypothesis test to determine if you agree that the mean
entry-level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.

Short Answer

Expert verified

1. The null hypothesis is given by, $H_{0}:\mu_{1}\geq \mu_{2}$

2. Alternate hypothesis is given by, $H_{a}:\mu_{1}< \mu_{2}$

3. \(\bar{X_{1}}-\bar{X-{2}} The difference between the mean entry level salaries of mechanical engineers and electrical engineers.

4. Student’s t distribution.

5. The paired test static for the mean difference is,

After ENTER all values the OUTPUT shown below,

6. The p-value from the output is $0.2066$

7. Using the information from previous exercise to sketch a picture of this situation.

Clearly label and scale the horizontal axis, and shade the graph the region(s) corresponding to the $p-$value.

8. $\alpha=0.05$

Decision: Null hypothesis is not rejected.

$p-value>alpha$

Conclusion: At the $5%$ level of significance, there is enough proof to conclude that mean entry-level salaries of mechanical engineers is less than that of electrical engineers.

Step by step solution

Step 1. Given information

Mean salaries are $\$46,100$ and $\$46,700$

Step 2. Calculation