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 54 entry level electrical engineers. Their mean salaries were $46,000 and $46,900, respectively. Their standard deviations were $3450 and $4210, 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.

1. In words, state what your random variable X_m − X_e represents.

a. X_m − X_e represents the mean starting salary of entry-level mechanical engineers and electrical engineers.

b. X_m − X_e represents the difference in starting salaries of entry-level mechanical engineers and electrical engineers.    

c. X_m − X_e represents the mean difference in the starting salaries of entry-level mechanical engineers and electrical engineers.

d. X_m − X_e represents the difference in the mean starting salaries of entry-level mechanical engineers and electrical engineers.

2.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

3.What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.

4.What is the p-value? (Round your answer to four decimal places.

5. Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.

6. Explain how you determined which distribution to use.

a. The t-distribution will be used because the samples are dependent.

b. The standard normal distribution will be used because the samples involve the difference in proportions.    

c. The standard normal distribution will be used because the samples are independent and the population standard deviation is known.

d. The t-distribution will be used because the samples are independent and the population standard deviation is not known.

Answer 1