Question

# The administration at your college announces that, on average, commuting students live farther than 30 miles...

The administration at your college announces that, on average, commuting students live farther than 30 miles from campus. The announcement came as somewhat of a surprise and took place at a press conference where it was important to make the point that the college attracts students who live 'far' from campus. A student advocacy group takes a random sample of 9 commuting students and records how far, in miles, they live from campus: 19,22,25,28,30,35,40,46,50.

a. Write a set of appropriate hypotheses.

b. Give the distribution of the appropriate random variable and give the distribution used in performing the hypotheses test. Are all assumptions met? Explain.

c. Find the critical value(s) for a pre-set a of 0.10.

d. For a = 0.10, make a decision and give a conclusion.

e. Based on this evidence, did the administration make a misleading claim at the press conference regarding the average commute distance from students? Explain.

a)

as test statistic is in critical region we reject null hypothesis and conclude that mean weight is different from 85.

b)

 for 95% CI; and 11 degree of freedom, value of t= 2.201 margin of error E=t*std error                            = 1.588 lower confidence bound=sample mean-margin of error = 81.61 Upper confidence bound=sample mean+margin of error= 84.79

as our confidence interval values does not contain 85 which signifies that mean is different from 85.

c)

for both of the interval and test is based on same cutoff region; therefore a and b gives the same result and not  contradictory