At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 36% 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, 45 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 36%.

Two different blood pressure medicines are being compared to determine if the average reduction in blood pressure is the same for each medication. The goal of the study is to determine if the medications differ. Twenty men age 50-60 years old are selected for the study. Ten men are chosen at random to receive the first medication and the other 10 men receive the second medication. Each of the 20 men is monitored for one month to determine the change in blood pressure over that time. Minitab provides the 95% confidence interval for (mu1 - mu2) (2.63, 14.18) a. Interpret this 95% CI. b. What assumptions (be specific) are necessary to construct this CI?

In the Texas senate races, a candidate must clear 50% to avoid a runoff election. In a recent poll of 1040 voters in Texas, 51% of voters preferred candidate. We will a hypothesis test to see if we can say at the 5% significance level that more than 50% of voters in Texas prefer candidate based on this poll. State the null and alternative hypothesis. Find the test-statistic. Find the P-value. Make a conclusion. Interpret your answer.

A poll found that 59​% of a sample of 1020 teens in a certain large country go online several times a day.​ (Treat this sample as a simple random​ sample.) Complete parts a through e below.   Find the margin of error for this poll if we want 90​% confidence in our estimate of the percent of teens in the country who go online several times a day.   Explain what the margin of error means.   If instead we need to be 95​% confident, will the margin of error be larger or​ smaller? Explain.    Find that margin of error.