An administrator at a rural college claims that theproportion,p, of students who commute farther than fifteen miles to school is more than15%. To test this, she selects a random sample of255 students at this college, and she finds that41 commute farther than fifteen miles to school, Is there enough evidence to support the administrator's claim at the0.10 level of significance?

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult alist of formulas.)

(a)State the null hypothesisH0 and the alternative hypothesisH1.

H0:

H1:

(b)Determine the type of test statistic to use.

(c)Find the value of the test statistic.

(d)Find thep-value.

(e)Can we support the claim that the proportion of students who commute farther than fifteen miles to school is more than15%?