At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 43% 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 170 students who visited the site looking for a roommate. Of the students surveyed, 60 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 0.10 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 43%. (a) State the null hypothesis Ho and the alternative hypothesis A, that you would use for the test. Ho: D P H 1 : 0 0 020 0-0 0#0 X (b) For your hypothesis test, you will use a Z-test. Find the values of mp and n (1 -p) to confirm that a Z-test can be used. (One standard is that np 2 10 and n (1-p) 2 10 under the assumption that the null hypothesis is true.) Here n is the sample size and p is the population proportion you are testing. np =0 X n(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 -P P (1 - p ) n 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 03- Step 2: Enter the test statistic. (Round to 3 decimal places.) 0.2 Step 3: Shade the area represented by he p-value. 0.1 - Step 4: Enter the p-value. (Round to 3 decimal places.) - 3 X 5 (d) Based on your answer to part (c), choose what can be concluded, at the 0.10 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 43% 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 43% 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 43% of students will find a match their first time using the site. O 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 43% of students will find a match their first time using the site