1.	A medical researcher wants to test whether there exists no connection between smoking and heart disease because the mean age at which heart disease is first detected is the same for smokers and nonsmokers. Some 20 smokers were matched with 20 non smokers according to age, lifestyle, medical history, occupation sex and so on. The researcher wants a significance level of .05. The average difference (Smokers minus nonsmokers) was -6 years. The standard deviation of the difference is 12 years. Formulate the null and alternate hypothesis Select the test statistic and note which table you will look up and calculate all relevant variables necessary to compute the test statistic: Give your decision rule and draw a graph which shows the areas of acceptance and rejection. Compare your calculations to your decision rule and show where it is on the graph. What are your conclusions? (Elaborate in terms of the problem studied.)
2.	One government official believed that for-profit nursing homes tend to discriminate between patients who pay themselves and patients who are supported by Medicaid by forcing Medicaid patients to leave the nursing home faster . 18 nursing homes were tested. 11 were nonprofit with mean Medicaid patient days of 75.4 and standard deviation of 16.3 days. 7 were for-profit with mean Medicaid patient days of 40.4 and standard deviation of 30.8 days. Use a .01 significance level. Formulate the null and alternate hypothesis Select the test statistic and note which table you will look up and calculate all relevant variables necessary to compute the test statistic: Give your decision rule and draw a graph which shows the areas of acceptance and rejection. Compare your calculations to your decision rule and show where it is on the graph. What are your conclusions? (Elaborate in terms of the problem studied.)
3.	NBC wants to know whether there is any difference in the proportion of males or females who favor Seinfeld. Two random samples of 80 males and 80 females were taken. 60% of the males were watching Seinfeld. 70% of the females were watching Seinfeld. The standard error of the proportion is .0675. NBC wants a significance of .15. Formulate the null and alternate hypothesis Select the test statistic and note which table you will look up and calculate all relevant variables necessary to compute the test statistic: Give your decision rule and draw a graph which shows the areas of acceptance and rejection. Compare your calculations to your decision rule and show where it is on the graph. What are your conclusions? (Elaborate in terms of the problem studied.)     The following is computer output from a linear regression from campaign expenditures and the number of votes gotten in the 1996 primaries: Expenditures ($) Votes           4000 60000           16000 60000           24000 180000           40000 660000           68000 540000           84000 420000           108000 900000           124000 600000           156000 660000           200000 720000                       Campaign Spending and Votes                       Regression Statistics Standard Error of Prediction 204505.6   Correlation Coefficient 0.749405459           R Square 0.561608542           Adjusted R Square 0.50680961           Standard Error 204505.6114           Observations 10                       ANOVA               df SS MS F Significance F   Regression 1 4.2862E+11 4.29E+11 10.24853 0.012587   Residual 8 3.3458E+11 4.18E+10       Total 9 7.632E+11                       Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 201815.8611 108320.0399 1.863144 0.099449 -47970.8 451602.5 X Variable 1 3.376021103 1.054567416 3.201333 0.012587 0.944183 5.807859 What is the relationship between votes and campaign expenditures? Explain it in words that the general public will understand.  What is the dependent variable? What is the independent variable? What is the slope? What does it tell you about the relationship between the two variables? At the .05 significance level can we say b does not equal 0? Circle the relevant data on the print-out. What is the intercept? What does it tell you about the relationship between expenditures and votes? What is the coefficient of determination or R square? What does it tell you about this regression model? If a candidate calculates that she needs 2.1 million votes to win the State of Washington. How much should she spend on her campaign? What judgments would you make about this prediction? A random sample of people were asked whether they preferred Brand A, B, C, or D. After the results were obtained, they were tabulated by gender. The market researchers want to determine if gender (being male or female) affects brand preference. Using the data construct a table to calculate a Chi-square which shows observed frequencies versus expected frequencies: Brand A Brand B Brand C Brand D Male 18 25 15 2 Female 32 5 1 2 Calculate the Chi-square and show all your work. Test this statistic to the .01 level. c) State your conclusions to the management of the company.

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