At a nearby college, there is a school-sponsored website that matches people looking for roommates. According to the school's reports, 44% 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 0.05 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 44%. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. Ho: O Â H₁:0 p np=0 n(1-p) = 0<0 OSO 020 ローロ ロメロ 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≥ 10 and 22 (1-p) 10 under the assumption that the null hypothesis is true.) Here is the sample size and p is the population proportion you are testing. S O>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) n The p-value is two times the area under the curve to the left of the value of the test statistic. Español 7 ∞ B

As part of a statistics project, Charlie would like to collect data on household size in his city. To do so, he asks each person in his statistics class for the size of their household and reports the results of a simple random sample. However, this is not a simple random sample. Why? O Charlie did not use any randomization; he took a convenience sample. O Charlie did not use a random number table to randomize the order in which he collected the students' responses, so the sample cannot be random. O In this investigation of household size, each household represents a case. Charlie incorrectly sampled individuals instead of households. OBoth (a) and (c) are correct. O Answers (a), (b), and (c) are all correct.

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?

A team of researchers would like to determine whether the number of households that use the internet for more than an hour a day is greater in large cities or small towns. To do so, the researchers take two random samples. The first sample consists of randomly selected people who live in cities with more than 500,000 people around the country. The second sample consists of randomly selected people who live in towns with fewer than 20,000 people. Are these samples dependent or independent? Select the correct answer below: O These samples are independent. O These samples are dependent. Not enough information is provided to determine independence.

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.

For several decades, it was a common practice in Southern California for houses to be built with pools in the backyard (as any airplane flight which ends at a Southern California airport will reveal). Now, however, that practice may be changing, possibly because of the recent demand for landscaped homes, which experts believe help reduce pollution. A recent study examined a random sample of  167  houses built in Southern California between 1950 and 1985 and an independent, random sample of  80  houses built in Southern California from 1992 to the present. The sample of houses built in 1950-1985 contained  71  houses with pools, and the sample of houses built from 1992-present contained  31  houses with pools. Based on this survey, can we conclude, at the  0.05  level of significance, that the proportion  p1  of all Southern California houses built in 1950-1985 that were built with pools is greater than the proportion  p2  of all Southern California houses built from…

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Please advise. Keep on tossing a coin until one gets a head.  List 2 possible outcomes from this sample.

2. In a population it is estimated that 20% have a desired trait of interest for the researcher. The researcher wants to know how many people on average he has to draw from a population to get 2 people with the trait. Use rows 20-24 of the Random Number Table to carry out the simulation. Explain clearly how you set up the problem and report your findings. Answer:

The local Hannaford is tracking mask compliance in their stores. In mid-March they found that only 40% of customers were wearing masks. They want to know if that percentage increased with the government mandates in place. Select the correct symbols to write the alternate hypothesis for this hypothesis test. Ha: