Question 1

A student at a four-year college claims that average enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 two-year colleges surveyed, the average enrollment was5065with a standard deviation of4778. Of the 35 four-year colleges surveyed, the average enrollment was5516with a standard deviation of8121. Conduct a hypothesis test at the 5% level.

NOTE: If you are using a Student'st-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 a

State the distribution to use for the test. (Enter your answer in the formzort_dfwheredfis the degrees of freedom. Round your answer to two decimal places.)

___________

Part b

State the distribution to use for the test. (Enter your answer in the formzort_dfwheredfis the degrees of freedom. Round your answer to two decimal places.)

t = ________

Part c

What is thep-value? (Round your answer to four decimal places.)

p= ______

part d

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

Question 2

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 surveys42entry level mechanical engineers and56entry level electrical engineers. Their mean salaries were$46,000and$46,900, respectively. Their standard deviations were$3420and$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 subscriptm= mechanicalande= electrical.

NOTE: If you are using a Student'st-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 a

State the distribution to use for the test. (Enter your answer in the formzort_dfwheredfis the degrees of freedom. Round your answer to two decimal places.)

______________

part b

What is the test statistic? (If using thezdistribution round your answer to two decimal places, and if using thetdistribution round your answer to three decimal places.)

t= __________

part c

What is thep-value? (Round your answer to four decimal places.)

p=_____________

Question 3

Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of31mpgwith a standard deviation of8mpg.Thirty-one non-hybrid sedans get a mean of20mpgwith a standard deviation ofthreempg.Suppose that the population standard deviations are known to be six and three, respectively. Conduct a hypothesis test at the 5% level to evaluate the manufacturers claim.

NOTE: If you are using a Student'st-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 a

What is the test statistic? (If using thezdistribution round your answer to two decimal places, and if using thetdistribution round your answer to three decimal places.)

z=_________

part b

What is thep-value? (Round your answer to four decimal places.)

p=________________

Thank you for your help. As you can see I'm struggling in a very particular spot.