At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 38% of students will find a match their first time using the site. A writer for the school newspaper tests this claim by choosing a random sampl_e of 165 students who visited the site looking for a roommate. Of the students surveyed, 77 said they found a match their first time using the site. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to reject the claim that the proportion,p, of all students who will find a match their first time using the site is 38%. (a) State the null hypothesis H0 and the alternative hypothesis H1 that you would use for the test. . /\\ C H0. p p E H1: 2 _=' _' X 6) \\ (b) For your hypothesis test, you will use a Z-test. Find the values of np and n(1p) to confirm that a Z-test can be used. (One standard is that npz 10 and n(1-p)210 under the assumption that the null hypothesis is true.) Here n is the sample size andp is the p_opulation proportion you are testing. np=|: X f) n(1p)=|: (c) F V n a Z-test. Here is some information to help you with your Z-test. . 20025 is the value that cuts off an area of 0.025 in the right tail of the distribution. /\\ P 'P 110-12) n - The value of the test statistic is given by z= Standard Normal Distribution Step 1: Select one-tailed or twotailed. O Onetailed O Two-tailed Step 2: Enter the critical value(s). (Round to 3 decimal places.) Cl Step 3: Enter the test statistic. (Round to 3 decimal places.) l:l (d) Based on your answer to part (c), choose what can be concluded, at the 0.05 level of significance, about the claim made in the school's reports. 0 Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to reject the claim that 38% of students will find a match their first time using the site. 0 Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to reject the claim that 38% of students will find a match their first time using the site. 0 Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is enough evidence to reject the claim that 38% of students will find a match their first time using the site. 0 Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to reject the claim that 38% of students will find a match their first time using the site