SHOW ALL YOUR WORKING:

1) A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If this is to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network receives 827 responses, of which 428 indicate they would like to see the new show in the lineup. Setup appropriate null and alternative hypotheses to test if the television network should give its newest show a spot during prime time at night?

2) A real estate investor thinks the real estate market has bottomed out. One of the variables he examined to arrive at this conclusion was the proportion of houses sold at or above the asking price. In 2010, the proportion of houses sold at or above the asking price was 14%. The real estate investor takes a random sample of 40 recently sold houses and finds that nine of them are selling at or above the asking price. Specify the null and alternative hypotheses to determine whether the proportion of houses sold at or above the asking price has increased. At the 10% significance level, can you conclude that the proportion of houses sold at or above the asking price has increased? (Make sure to follow all procedures for hypothesis testing to answer this)

3) An analyst conducts a hypothesis test to check whether the mean return for a particular fund differs from 10%. He assumes that returns are normally distributed and sets up the following competing hypotheses: Ho: = 10,HA: 10. Over the past 10 years the fund has had an average annual return of 13.4% with a standard deviation of 2.6%. The value of the test statistic is 4.14 and the critical values at the 5% significance level are2.262 and 2.262.Based on these conditions, state the correct decision (or conclusion).

4) A city is considering widening a busy intersection in town. Last year, the city reported 16,000 cars passed through the intersection per day. The city conducted a survey for 49 days this year and found an average of 17,000 cars passed through the intersection, with a standard deviation of 5,000. Specify the null and alternative hypotheses to determine whether the intersection has seen an increase in traffic. The city is going to widen the intersection if it believes traffic has increased. At the 5% significance level, can you conclude that the intersection has seen an increase in traffic? Should the city widen the intersection?

5) The serious delinquency rate measures the proportion of homes that are well behind on their mortgage payments. A real estate investor is trying to decide in which of two neighborhoods in Phoenix to buy an investment property. He is trying to decide if the serious delinquency rate differs between the two neighborhoods. He took a sample of 70 homes in neighborhood 1 and found 14 homes were seriously delinquent. He took a sample of 80 homes in neighborhood 2 and 10 homes were seriously delinquent. Specify the null and alternate hypotheses to determine if the delinquency rates in the two neighborhoods are equal and make a conclusion at the 10% significance level. How should the delinquency rate influence the investor's decision? (Make sure to follow all procedures for hypothesis testing)