An administrator at a rural college claims that the proportion, p, of students who commute farther than fifteen miles to school is more than 15%. To test this, she selects a random sample of 265 students at this college, and she finds that 50 commute farther than fifteen miles to school, Is there enough evidence to support the administrator's claim at the 0.10 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 a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H. O P H : 0 X S p H :0 (b) Determine the type of test statistic to use. (Choose one) 0=0 50 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) x 00 0 X 5 ? (d) Find the critical value. (Round to three or more decimal places.) 0 (e) Can we support the claim that the proportion of students who commute farther than fifteen miles to school is more than 15%? O Yes ONo