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Student t test and rank correlation

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(See attached file for full problem description)

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Be sure to answer all the following questions for each Problem.
(a) Write the claim mathematically and identify H0 and H1:
(b) Find the critical values (CVs) and identify the rejection regions:
(c) Find the test statistic (TS):
(d) Decide whether to reject or fail to reject H0:
(e) Determine the p-value for the hypothesis test:
(f) Interpret the decision in the context of the original claim:
16. A recent study compared the time spent together by single-and dual-earner couples. According to the records kept by the wives during the study, the mean amount of time spent together watching television among the single-earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean number of minutes spent watching television was 48.4 minutes, with a standard deviation of 18.1 minutes. At the .01 significance level, can we conclude that the single-earner couples on average spend more time watching television together? There were 15 single-earner and 12 dual-earner couples studied.

22. The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results.

Number of Crimes by Area
A B C D E F G H
Before 14 7 4 5 17 12 8 9
After 2 7 3 6 8 13 3 5

Has there been a decrease in the number of crimes since the inauguration of the program? Use the .01 significance level. Estimate the p-value.

46. The following data on annual rates of return were collected from five stocks listed on the New York Stock Exchange ("the big board") and five stocks listed on NASDAQ. At the .10 significance level, can we conclude that the annual rates of return are higher on the big board?

NYSE NASDAQ
17.16 15.80
17.08 16.28
15.51 16.21
8.43 17.97
25.15 7.77