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Magazine 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
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鈥檚 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
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鈥檚 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.
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