A college claims that the proportion, p, of students who commute more than fifteen miles to school is less than 20%. A researcher wants to test this. A random sample of 275 students at this college is selected, and it is found that 51 commute more than fifteen miles to school. Is there enough evidence to support the college's claim at the 0.01 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H. and the alternative hypothesis H₁. H:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Is there enough evidence to support the claim that the proportion of students who commute more than fifteen miles to school is less than 20%? O Yes O No H |x X a S 0° 0 X =O OSO □<口 P ô 믐 20 >O

The hypothesized percentage of students, who commute more than fifteen miles, $p_0=20\mathrm{\%}$ (or $0.20$).

The sampled number of students, $n=275$.

The sampled number of students, who commute more than fifteen miles, $x=51$.

The significance level, $\alpha =0.01$.