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Statistics Winter 2005 Section 08 Dr. Redmond Name_________________________ 1. The grade point averages of students participating in sports at a local college are to be compared. The data are listed below. Tennis Golf Swimming 2.1 1.8 3.0 3.2 2.1 2.5 2.5 1.9 2.8 3.5 3.3 2.7 3.1 2.5 2.6 Perform an analysis of variance test and give the P-value. Write down exactly what R gives you, without rounding. _______________________ 2. What is your conclusion to the sports problem above? (Use .01.) a) There is evidence of a connection between grade point average and sport. b) There is not enough evidence to conclude that there is a connection between grade point average and sport. 3. As part of a marketing experiment, a department store regularly mailed discount coupons to 25 of its credit card holders. Their total credit card purchases over the next three months were compared to their credit card purchases during the previous three months. The amount of each customer’s purchases over the next three months was subtracted from the amount of his or her purchases over the previous three months (previous minus next). You are attempting to prove that this marketing scheme (of mailing coupons) works. What is the alternative hypothesis for this test? a) H a : 0 b) H a : 0 c) H a : 0 d) H a : 0 4. A local brewery distributes beer in bottles labeled 12 ounces. Twenty of these bottles are selected and their contents are measured. The sample mean turns out to be 11.7 ounces with a standard deviation of 1.3 ounces. You are trying to prove that the average volume of a bottle of beer is less than 12 ounces. Find the confidence interval you would use for this test. Use .05. Write down exactly what R gives you, without rounding at all. SHOW ALL YOUR WORK. __________________________ 5. When performing a Chi-Square test, after computing the expected values, one must then go to each cell and calculate a special number that is a measure of how close the observed value of that cell is to the expected value of that cell. Suppose that in a particular cell you had an observed value of 26 and an expected value of 35. Calculate this special number for this cell. ROUND TO TWO DECIMAL PLACES. SHOW YOUR WORK. _____________________ 6. The engineering school at a major university claims that more than 20% of its graduates are women. In a graduating class of 210 students, 58 were women. You are attempting to support this claim. Find the confidence interval you would use for this test. Use .05. Write down exactly what R gives you, without rounding at all. __________________________ 7. Five students took the SAT. Their scores are listed below. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. Student 1 2 3 4 5 Scores before course 720 860 850 880 860 Scoresafter course 740 860 840 920 890 The claim is that the preparation course improves students scores on the average. You are attempting to support this claim. Calculate the P-value for this test. Write down exactly what R gives you, without rounding at all. _________________________ 8. Repeat the problem above, except now assume that the group of students who took the SAT without taking the preparation course is completely different from the group of students who took the SAT after taking the preparation course. Also, assume equal variances. (Again, calculate the P-value for this test. Write down exactly what R gives you, without rounding at all.) ___________________________ 9. A fast food outlet claims that the mean waiting time in line is less than 2.1 minutes. A random sample of 20 customers has a mean of 1.9 minutes with a standard deviation of 1.1 minutes. You are attempting to support this claim. Find the P-value you would use for this test. Write down exactly what R gives you, without rounding at all. SHOW YOUR WORK. ___________________________ 10. A very large Chi-squared value leads to a a) small P-value. b) large P-value. 11. The following table gives the results of a poll taken to study the opinions of adults and teenagers on legal gambling. Approve Disapprove No Opinion Adults 959 488 76 Teens 261 235 5 What would be the alternative hypothesis for this test? a) There is a connection between age and opinion. b) There is no connection between age and opinion. 12. Use R to calculate the P-value for the data in the opinion problem above. Write down exactly what R gives you, without rounding. _________________________ 13. What is your conclusion to the opinion problem above? (Use .01.) a) There is evidence of a connection between age and opinion. b) There is not enough evidence to conclude that there is a connection between age and opinion. 14. A sports researcher is interested in determining if there is a relationship between the number of home team wins and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Football Basketball Soccer Baseball Home 39 156 25 83 Away 31 98 19 75 Use R to calculate the Chi-squared value for this data. Write down exactly what R gives you, without rounding. DO NOT DO THIS BY HAND. ______________________ 15. For the sports problem above, write down all of the expected values. Use R to do this. You may round to two decimal places. DO NOT DO THIS BY HAND. 16. The data below are the scores of 10 randomly selected students from a statistics class and the number of hours they studied for the exam. Hours, x 3 5 2 8 2 4 4 5 6 3 Scores, y 65 80 60 88 66 78 85 90 90 71 Find the correlation of x and y. Write down exactly what R gives you, without rounding at all. __________________________ 17. For the regression problem above, determine the P-value you would use to decide if there is enough evidence of a relationship between study time and score. Write down exactly what R gives you, without rounding at all. _________________________ 18. For the regression problem above, write down the equation of the regression line. Do not round at all. __________________________ 19. For the regression problem above, plot x vs. y, along with the graph of the regression line. I will come by to check this. 20. Find a 90% prediction interval for the score of a student who studies for seven hours. Write down exactly what R gives you, without rounding at all. ___________________________ 21. Consider a Chi-Square Table with two rows and three columns. Suppose also the following: -The sum of the numbers in the first row is 102. -The sum of the numbers in the second row is 70. -The sum of the numbers in the first column is 55. -The sum of the numbers in the second column is 33. -The sum of the numbers in the third column is 84. -The observed value for the cell in the first row and second column is 20. Calculate the expected value for the cell in the first row and second column. ROUND TO TWO DECIMAL PLACES. _____________________ 22. A realtor wishes to compare the average square footage of houses in 4 different cities by doing an analysis of variance test. The null hypothesis for this test would be a) The average square footage is the same for each city. b) There is a connection between square footage and location. c) The average square footage is different for each city. 23. In an area of the Midwest, records were kept on the relationship between the rainfall in inches (x) and the yield of wheat in bushels (y). The following regression equation is determined: y 4.379x 4.267 ˆ Use this equation to predict the yield of wheat if eleven inches of rain falls. Do not round at all. ___________________________ 24. To test the effectiveness of a new drug designed to relieve pain, 200 patients were randomly selected and divided into two equal groups. One group of 100 patients was given a pill containing the drug while the other group of 100 was given a placebo. There were 62 patients who actually took the drug and felt relief from their symptoms, while 41 of the patients taking the placebo felt relief. You are to perform a two-tailed test to see if there is evidence of a difference between the true proportion of patients taking the drug and experiencing relief and the true proportion of patients taking the placebo and experiencing relief. Calculate the P-value for this test. Write down exactly what R gives you, without rounding at all. ____________________________ 25. In a survey of 500 doctors that practice medicine, 20% felt that the government should control health care. In a survey of 800 doctors that were general practitioners, 30% felt that the government should control health care. You are to perform a two-tailed test to see if there is evidence of a difference between the true proportions. Calculate the P-value for this test. Write down exactly what R gives you, without rounding at all. ____________________________