Name: Partners: Statistics. Review 11 Version A

Transcription

1 Name: Partners: Statistics Date: Review 11 Version A [A] Circle whether each statement is true or false. 1. An ANOVA is an F test of two variances. 2. Extrapolation often yields unrealistic results. 3. The peak of a ç 2 distribution is at ç 2 = n The lowest possible value of ç 2 and of F is zero. 5. If r = 1 or -1, then y can be perfectly predicted by x. 6. In a ç 2 test of independence, both variables are discrete. 7. In a negative correlation, lower values of x predict lower values of y. 8. For the data sets {4, 5, 6}, {5, 6, 7}, and {5, 7, 9}, MS W = ( ) If a group of 80 people includes 44 males and 60 skiers, E for male skiers is ANOVA tests if there is significantly more variance between samples than within samples. 11. The data do not come from a normal distribution could be the null hypothesis in a ç 2 goodness of fit test. 12. A reasonable estimate for the correlation coefficient between time spent studying and time spent using social media is [B] Sarah measures the resting heart rate of nine senior girls and times them in a mile run. participant # resting heart rate: mile time (seconds): Calculate r in a right-tailed test. 2. What does the fact that the correlation is positive mean about the relationship between resting heart rate and mile time? 3. State Sarah s conclusion, followed by r and a range for p. 4. What is the equation of the line of best fit for Sarah s data? 5. Would it make more sense to use this line of best fit to predict the mile time of a girl with a resting heart rate of 40 or of 60? Explain your answer using the words interpolation and extrapolation. 6. What mile time would be predicted by the line of best fit for the resting heart rate you chose in #5? Express your answer in standard min:sec format (e.g., 7:30, not 7.5).

2 [C] For each research question, state the type of test, the critical value(s), the conclusion, and the p range, based on the sample size n and the calculated statistic X. X could represent z, t, r, ç 2, or F. 1. Do people write faster using cursive than printing? n = 9, X = Is there a relationship between alcohol consumption and intelligence? n = 16, X = Is the standard deviation of weekly number of visitors to Ziegler Zoo different from 100? n = 15, X = Does reaction time vary by profession (businessman, construction worker, musician)? n 1 = 12, n 2 = 16, n 3 = 7, X = Is there a relationship between favorite sport (football, baseball, basketball, or hockey) and favorite holiday (Halloween, Thanksgiving, or Christmas)? n = 75, X = Do college students get less than 7 hours of sleep per night on average? n = 25, X = [D] Officer Arana keeps track of the black, white, and colored cars that pass the summit on Highway 17. For each scenario, give a conclusion followed by the calculated statistics and a p value range. 1. The speeds of the first 20 cars (in mph) are 55, 59, 50, 56, 58, and 53 for the black cars, 38, 44, 53, 50, 56, 48, and 64 for the white cars, and 62, 68, 50, 64, 70, 50, and 59 for the colored cars. 2. Overall, 19 of the black cars are sedans, 25 are coups, and 12 are other; 25 of the white cars are sedans, 5 are coups, and 4 are other, and 19 of the colored cars are sedans, 15 are coupes, and 18 are other. [E] Do the following to organize your group s reviews. 1. Make sure your name and your partners names are at the top of your review the first day. 2. Staple the reviews in order, all facing the same way. Put the staple in the very top left corner if everyone is finished or if the review is due; otherwise put the staple in the top right corner.

3 Name: Statistics Date: Review 11 Version B [A] Circle whether each statement is true or false. 1. An ANOVA is an F test of two variances. 2. Extrapolation often yields unrealistic results. 3. The peak of a ç 2 distribution is at ç 2 = n The lowest possible value of ç 2 and of F is zero. 5. If r = 1 or -1, then y can be perfectly predicted by x. 6. In a ç 2 test of independence, both variables are discrete. 7. In a negative correlation, lower values of x predict lower values of y. 8. For the data sets {4, 5, 6}, {5, 6, 7}, and {5, 7, 9}, MS W = ( ) If a group of 80 people includes 44 males and 60 skiers, E for male skiers is ANOVA tests if there is significantly more variance between samples than within samples. 11. The data do not come from a normal distribution could be the null hypothesis in a ç 2 goodness of fit test. 12. A reasonable estimate for the correlation coefficient between time spent studying and time spent using social media is [B] Sarah measures the resting heart rate of nine senior girls and times them in a mile run. participant # resting heart rate: mile time (minutes) Calculate r in a right-tailed test. 2. What does the fact that the correlation is positive mean about the relationship between resting heart rate and mile time? 3. State Sarah s conclusion, followed by r and a range for p. 4. What is the equation of the line of best fit for Sarah s data? 5. Would it make more sense to use this line of best fit to predict the mile time of a girl with a resting heart rate of 40 or of 60? Explain your answer using the words interpolation and extrapolation. 6. What mile time would be predicted by the line of best fit for the resting heart rate you chose in #5? Express your answer in standard min:sec format (e.g., 7:30, not 7.5).

4 [C] For each research question, state the type of test, the critical value(s), the conclusion, and the p range, based on the sample size n and the calculated statistic X. X could represent z, t, r, ç 2, or F. 1. Do people write faster using cursive than printing? n = 25, X = Is there a relationship between alcohol consumption and intelligence? n = 20, X = Is the standard deviation of weekly number of visitors to Ziegler Zoo different from 100? n = 21, X = Does reaction time vary by profession (businessman, construction worker, musician)? n 1 = 15, n 2 = 16, n 3 = 17, X = Is there a relationship between favorite sport (football, baseball, basketball, or hockey) and favorite holiday (Halloween, Thanksgiving, or Christmas)? n = 108, X = Which gender is more likely to vote for McDermott for president? n 1 = 45, n 2 = 53, X = 0.98 [D] Officer Arana keeps track of the black, white, and colored cars that pass the summit on Highway 17. For each scenario, give a conclusion followed by the calculated statistics and a p value range. 1. The speeds of the first 25 cars (in mph) are 60, 55, 54, 51, 55, 52, and 54 for the black cars, 54, 48, 55, 49, 52, 56, and 59 for the white cars, and 54, 60, 60, 56, 57, 58, 60, and 58 for the colored cars. 2. Overall, 14 of the black cars are sedans, 16 are coups, and 9 are other; 31 of the white cars are sedans, 16 are coups, and 14 are other, and 19 of the colored cars are sedans, 12 are coupes, and 11 are other. [E] Bonus. 1. Redo problem [D] #1, adding a red car going 99 mph. a) State the new conclusion, the new F, and the new p range. b) Explain why adding the really fast car caused this change in result.

5 Name: Statistics Date: Review 11 Version C [A] Circle whether each statement is true or false. 1. An ANOVA is an F test of two variances. 2. Extrapolation often yields unrealistic results. 3. The peak of a ç 2 distribution is at ç 2 = n The lowest possible value of ç 2 and of F is zero. 5. If r = 1 or -1, then y can be perfectly predicted by x. 6. In a ç 2 test of independence, both variables are discrete. 7. In a negative correlation, lower values of x predict lower values of y. 8. For the data sets {4, 5, 6}, {5, 6, 7}, and {5, 7, 9}, MS W = ( ) If a group of 80 people includes 44 males and 60 skiers, E for male skiers is ANOVA tests if there is significantly more variance between samples than within samples. 11. The data do not come from a normal distribution could be the null hypothesis in a ç 2 goodness of fit test. 12. A reasonable estimate for the correlation coefficient between time spent studying and time spent using social media is [B] Sarah measures the resting heart rate of nine senior girls and times them in a mile run. participant # resting heart rate: average speed (mph): Calculate r in a left-tailed test. 2. What does the fact that the correlation is negative mean about the relationship between resting heart rate and speed? 3. State Sarah s conclusion, followed by r and a range for p. 4. What is the equation of the line of best fit for Sarah s data? 5. Would it make more sense to use this line of best fit to predict the mile time of a girl with a resting heart rate of 40 or of 60? Explain your answer using the words interpolation and extrapolation. 6. What mile time would be predicted by the line of best fit for the resting heart rate you chose in #5? Express your answer in standard min:sec format (e.g., 7:30, not 7.5).

6 [C] For each research question, state the type of test, the critical value(s), the conclusion, and the p range, based on the sample size n and the calculated statistic X. X could represent z, t, r, ç 2, or F. 1. Do people write faster using cursive than printing? n = 77, X = Is there a relationship between alcohol consumption and intelligence? n = 18, X = Is the standard deviation of weekly number of visitors to Ziegler Zoo different from 100? n = 24, X = Does reaction time vary by profession (businessman, construction worker, musician)? n 1 = 8, n 2 = 6, n 3 = 6, X = Is there a relationship between favorite sport (football, baseball, basketball, or hockey) and favorite holiday (Halloween, Thanksgiving, or Christmas)? n = 114, X = Using 6 categories, are speeds on Highway 17 not normally distributed? n = 196, X = 9.36 [D] Officer Arana keeps track of the black, white, and colored cars that pass the summit on Highway 17. For each scenario, give a conclusion followed by the calculated statistics and a p value range. 1. The speeds of the first 24 cars (in mph) are 53, 50, 48, 55, 56, 53, and 55, for the black cars, 50, 50, 53, 47, 49, 52, 52, and 59 for the white cars, and 54, 59, 57, 62, 50, 54, 54, 56, and 59 for the colored cars. 2. Overall, 14 of the black cars are sedans, 7 are coups, and 8 are other; 13 of the white cars are sedans, 7 are coups, and 6 are other, and 15 of the colored cars are sedans, 9 are coupes, and 14 are other. [E] Bonus. 1. Redo problem [D] #1, adding a red car going 99 mph. a) State the new conclusion, the new F, and the new p range. b) Explain why adding the really fast car caused this change in result.

7 Name: Statistics Date: Review 11 Version D [A] Circle whether each statement is true or false. 1. An ANOVA is an F test of two variances. 2. Extrapolation often yields unrealistic results. 3. The peak of a ç 2 distribution is at ç 2 = n The lowest possible value of ç 2 and of F is zero. 5. If r = 1 or -1, then y can be perfectly predicted by x. 6. In a ç 2 test of independence, both variables are discrete. 7. In a negative correlation, lower values of x predict lower values of y. 8. For the data sets {4, 5, 6}, {5, 6, 7}, and {5, 7, 9}, MS W = ( ) If a group of 80 people includes 44 males and 60 skiers, E for male skiers is ANOVA tests if there is significantly more variance between samples than within samples. 11. The data do not come from a normal distribution could be the null hypothesis in a ç 2 goodness of fit test. 12. A reasonable estimate for the correlation coefficient between time spent studying and time spent using social media is [B] Sarah measures the resting heart rate of nine senior girls and times them in a mile run. participant # resting heart rate: mile time (min:sec): 7:30 6:24 8:15 9:50 5:24 5:49 6:30 7:21 9:58 1. Calculate r in a right-tailed test. 2. What does the fact that the correlation is positive mean about the relationship between resting heart rate and mile time? 3. State Sarah s conclusion, followed by r and a range for p. 4. What is the equation of the line of best fit for Sarah s data? 5. Would it make more sense to use this line of best fit to predict the mile time of a girl with a resting heart rate of 40 or of 60? Explain your answer using the words interpolation and extrapolation. 6. What mile time would be predicted by the line of best fit for the resting heart rate you chose in #5? Express your answer in standard min:sec format (e.g., 7:30, not 7.5).

8 [C] For each research question, state the type of test, the critical value(s), the conclusion, and the p range, based on the sample size n and the calculated statistic X. X could represent z, t, r, ç 2, or F. 1. Do people write faster using cursive than printing? n = 205, X = Is there a relationship between alcohol consumption and intelligence? n = 6, X = Is the standard deviation of weekly number of visitors to Ziegler Zoo different from 100? n = 62, X = Does reaction time vary by profession (businessman, construction worker, musician)? n 1 = 10, n 2 = 10, n 3 = 10, X = Is there a relationship between favorite sport (football, baseball, basketball, hockey, or other) and favorite holiday (Halloween, Thanksgiving, Christmas, or other)? n = 175, X = Does Professor McFall grade more consistently than Professor Frosty? n 1 = 16, n 2 = 20, X = 4.89 [D] Officer Arana keeps track of the black, white, and colored cars that pass the summit on Highway 17. For each scenario, give a conclusion followed by the calculated statistics and a p value range. 1. The speeds of the first 22 cars (in mph) are 45, 50, 53, 54, 56, 51, and 55 for the black cars, 45, 49, 56, 52, 48, 49, and 53 for the white cars, and 55, 59, 53, 52, 60, 59, 56, and 56 for the colored cars. 2. Overall, 20 of the black cars are sedans, 11 are coups, and 12 are other; 25 of the white cars are sedans, 7 are coups, and 4 are other, and 19 of the colored cars are sedans, 15 are coupes, and 14 are other. [E] Bonus. 1. Redo problem [D] #1, adding a red car going 99 mph. a) State the new conclusion, the new F, and the new p range. b) Explain why adding the really fast car caused this change in result.