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 52 entry level electrical engineers. Their mean salaries were $46,100 and $46,900, respectively. Their standard deviations were $3430 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. 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.) Part 1) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. Part 2) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) ? =   Part 3)Explain how you determined which distribution to use. a)The t-distribution will be used because the samples are independent and the population standard deviation is not known. b)The t-distribution will be used because the samples are dependent.     c)The standard normal distribution will be used because the samples involve the difference in proportions. d)The standard normal distribution will be used because the samples are independent and the population standard deviation is known.

Hypothesis Testing- 2 samples

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 52 entry level electrical engineers. Their mean salaries were $46,100 and $46,900, respectively. Their standard deviations were $3430 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. 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.)

Part 1) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

Part 2) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.