At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 46% of students will find Espanic 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, 65 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 46% (a) State the null hypothesis Ho and the alternative hypothesis /, that you would use for the test. Ho: P P H: I 020 0-0 070 X ? (b) For your hypothesis test, you will use a Z-test. Find the values of np 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= 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