v At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 42% 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 sample of 160 students who visited the site looking for a roommate. Of the students surveyed, $3 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 42%. (a) State the null hypothesis Ho and the alternative hypothesis #, that you would use for the test. H: 020 0-0 020 2 (b) For your hypothesis test, you will use a Z-test. Find the values of ap and " (1-p) to confirm that a Z-test can be used. (One standard is that ap 2 10 and * (1-p) 2 10 under the assumption that the null hypothesis is true.) Here , is the sample size and p is the population proportion you are testing. mp= 0 X ? * (1-P)= 0 (c) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test. The value of the test statistic is given by P (1-P) The p-value is two times the area under the curve to the left of the value of the test statistic. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. o One-tailed O Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) Step 3: Shade the area represented by the p- value. Step 4: Enter the p- value. (Round to 3 decimal places.) * 5 ? (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. X ? Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to reject the claim that 42% of students will find a match their first time using the site. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to reject the claim that 42%% of students will find a match their first time using the site. Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to reject the claim that 42% of students will find a match their first time using the site. Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to reject the claim that 42% of students will find a match their first time using the site