User_type Gender student male student male student male student female student female student male student male student male student female student female student female student male student male student male student male student female student female student male student male student male student male student male student female student female student male student female student female student male student female student female student male student female student male student female student female student female student male student male student male student female student female student female student male student male student female Height Weight BMI BEPL AEPL 73 195 25.72 69 67 135 21.14 92 73 190 25.06 60 65 108 17.97 75 70 150 21.52 100 72 200 27.12 75 71 178 24.82 85 67 210 32.89 70 60 105 20.5 48 66 135 21.79 86 67 135 21.14 60 69 150 22.15 68 69 160 23.63 87 67 135 21.14 73 78 164 18.95 71 60 170 33.2 70 65 130 21.63 76 69 155 22.89 68 66 138 22.27 80 72 165 22.38 56 68 140 21.28 95 75 171 21.37 82 70 230 33 70 67 143 22.39 103 68 180 27.37 58 65 130 21.63 75 65 180 29.95 45 72 280 37.97 100 65 130 21.63 91 66 148 23.89 78 72 178 24.14 75 63 138 24.44 62 71 164 22.87 61 65 150 24.96 95 63 112 19.84 83 65 135 22.46 72 73 193 25.46 68 72 195 26.44 55 71 230 32.07 84 60 95 18.55 87 60 138 26.95 84 66 130 20.98 80 72 175 23.73 82 75 200 25 54 63 145 25.68 61 75 104 77 121 130 100 106 78 89 97 67 78 121 91 101 99 79 85 85 69 120 113 110 151 103 96 53 130 140 108 88 84 119 125 110 85 86 80 93 94 107 109 110 75 90 student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student female male male female female female female male female female male female female female male male female male female male female male male female male male female female female male male male male female male male female male female female male male female male male female 70 67 69 55 65 69 67 71 70 67 72 64 70.5 67 75 71 57 74 61 72 64 67 69 63 70 67 67 64 65.5 74 75 70 74 72 75 66 72 70 67 72 70 61 72 70 72 165 145 230 62 120 165 120 165 265 150 148 145 134 175 175 185 94 240 115.2 190 175 165 200 170 155 150 220 125 111 180 200 190 186 84 150 195 130 240 140 125 185 165 127 165 165 130 23.67 22.71 33.96 14.41 19.97 24.36 18.79 23.01 38.02 23.49 20.07 24.89 18.95 27.41 21.87 25.8 20.34 30.81 21.76 25.77 30.04 25.84 29.53 30.11 22.24 23.49 34.45 21.45 18.19 23.11 25 27.26 23.88 21.02 20.34 24.37 20.98 32.55 20.09 19.58 25.09 23.67 23.99 22.38 23.67 17.63 77 77 94 60 70 60 83 70 108 62 80 75 78 84 80 61 108 60 87 88 40 80 45 72 81 80 78 76 65 80 38 59 74 72 92 84 70 70 87 72 80 70 46 76 60 58 95 90 130 120 107 72 114 97 127 109 113 94 92 124 105 88 132 120 105 102 98 110 60 102 112 112 112 115 117 102 68 85 83 138 115 86 95 124 120 120 101 97 95 85 83 115 student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student male male female female male male male male male male female male male male female female male male female male male male female male female male female male female male female male female female female female male male female 75 70 66 65 72 64 73 68 71 53 68 69 86 70 70 51.5 73 70 65.5 71 68 69 65 66 69.6 69 64 69 54 72 60 63 65 67 62 64 72 67 67 315 170 130 117 190 145 195 165 215 65 140 145 220 250 220 52 154 170 119 165 145 170 150 170 145 175 142 225 118 190 104 142 114 150 145 103 160 160 135 39.37 24.39 20.98 19.47 25.77 24.89 25.72 25.09 29.98 16.27 21.28 21.41 20.91 35.87 31.56 13.78 20.32 24.39 19.5 23.01 22.04 25.1 24.96 27.44 21.04 25.84 24.37 33.22 28.45 25.77 20.31 25.15 18.97 23.49 26.52 17.68 21.7 25.06 21.14 85 76 63 81 83 65 108 68 66 114 80 77 69 66 91 72 86 77 77 67 70 72 70 85 100 85 87 88 75 81 71 61 65 67 75 95 79 62 91 145 92 59 150 95 90 121 103 102 150 117 106 97 117 135 144 126 106 108 110 88 96 86 130 120 110 99 126 115 96 102 87 85 80 106 98 95 123 144 User_type Guess student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student Actual 18 23 27 36 30 29 16 36 25 12 30 20 10 26 20 25 18 22 24 25 23 23 20 15 14 25 30 28 45 20 13 25 23 24 25 15 30 12 22 30 28 50 30 20 19 25 28 30 27 28 30 25 25 31 29 29 28 29 28 32 31 29 26 30 27 27 26 27 33 32 28 27 29 29 32 27 28 28 26 31 29 28 29 30 30 30 31 31 32 28 student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student instructor student student student student student student student student student student 15 20 12 28 20 16 55 15 18 15 50 15 12 38 25 40 16 45 20 39 22 25 35 12 24 24 30 20 25 24 20 23 24 19 30 18 37 24 15 40 35 18 18 24 20 27 32 27 31 30 31 33 29 30 31 29 33 25 29 28 28 34 30 25 25 33 35 30 26 28 29 31 28 26 34 31 24 33 25 28 32 29 34 27 34 32 34 39 29 36 33 32 student student student student student student student student instructor student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student 21 30 15 25 16 30 10 27 50 15 24 28 30 20 23 23 15 12 36 25 25 27 33 37 30 32 17 17 21 30 30 23 25 43 26 15 15 22 28 39 15 20 15 50 22 27 31 29 26 28 28 28 33 28 37 31 28 29 31 32 28 29 31 30 27 28 34 30 32 30 28 26 27 29 25 30 26 33 31 35 35 34 30 26 27 31 26 31 39 38 33 35 student student student student student student student student student student student student student 32 25 30 22 23 25 20 18 11 23 22 20 18 33 30 33 30 33 33 36 30 24 32 30 31 28 User_type Gender student male student male student female student female student male student male student female student female student male student male student male student male student female student female student male student male student male student male student female student female student male student female student male student female student female student male student female student female student female student female student male student male student male student female student female student male student male student female student female student male student male student female student female student female student female Height Weight BMI BEPL AEPL 67 135 21.14 92 73 190 25.06 60 65 108 17.97 75 70 150 21.52 100 72 200 27.12 75 71 178 24.82 85 60 105 20.5 48 66 135 21.79 86 69 150 22.15 72 69 160 23.63 87 67 135 21.14 73 78 164 18.95 71 60 170 33.2 70 65 130 21.63 76 69 155 22.89 68 72 165 22.38 56 68 140 21.28 95 75 171 21.37 82 70 230 33 70 67 143 22.39 103 68 180 27.37 58 65 130 21.63 75 72 280 37.97 100 65 130 21.63 91 66 148 23.89 78 72 178 24.14 75 63 138 24.44 62 65 150 24.96 95 63 112 19.84 83 65 135 22.46 77 73 193 25.46 68 72 195 26.44 55 71 230 32.07 84 60 138 26.95 84 66 130 20.98 80 72 175 23.73 82 75 200 25 54 63 145 25.68 61 70 165 23.67 77 67 145 22.71 77 69 230 33.96 94 55 62 14.41 80 65 120 19.97 70 69 165 24.36 60 67 120 18.79 83 RateChange 104 12 77 17 121 46 130 30 100 25 106 21 89 41 107 21 80 8 121 34 91 18 101 30 99 29 89 13 85 17 79 23 120 25 113 31 110 40 151 48 103 45 96 21 130 30 120 29 108 30 88 13 84 22 125 30 110 27 85 8 86 18 80 25 113 29 107 23 109 29 110 28 75 21 90 29 95 18 90 13 130 36 110 30 107 37 82 22 114 31 student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student student male female female male female female female male male female female male female male male female male male female female female male male male male male female female female male male female male female male male male male male male male female male male male female 71 70 67 72 64 70.5 67 75 71 57 61 72 64 67 69 63 70 67 67 64 65.5 74 75 70 74 72 66 70 67 72 70 61 70 72 70 72 64 73 68 71 53 68 69 86 70 70 165 265 150 148 145 134 175 175 185 94 115.2 190 175 165 200 170 155 150 220 125 111 180 200 190 186 150 130 140 125 185 165 127 165 130 170 190 145 195 165 215 65 140 145 220 250 220 23.01 38.02 23.49 20.07 24.89 18.95 27.41 21.87 25.8 20.34 21.76 25.77 30.04 25.84 29.53 30.11 22.24 23.49 34.45 21.45 18.19 23.11 25 27.26 23.88 20.34 20.98 20.09 19.58 25.09 23.67 23.99 23.67 17.63 24.39 25.77 24.89 25.72 25.09 29.98 16.27 21.28 21.41 20.91 35.87 31.56 70 108 72 80 75 78 84 80 61 108 87 88 60 80 45 72 81 80 78 76 75 80 38 59 74 92 70 87 72 80 70 56 60 78 76 83 65 108 68 66 114 80 77 69 66 91 97 127 109 113 94 92 124 105 88 132 105 102 98 110 60 102 112 112 112 115 117 102 68 85 86 115 95 120 120 101 97 95 83 115 92 95 90 121 103 102 150 117 106 97 117 135 27 19 37 33 19 14 40 25 27 24 18 14 38 30 15 30 31 32 34 39 42 22 30 26 13 23 25 33 48 21 27 39 23 37 16 12 25 13 35 36 36 37 29 28 51 44 student student student student student student student student student student student student student student student student student student student male male female male male male female female male female male female male female male female female female male 73 70 65.5 71 68 69 65 69.6 69 64 69 54 72 60 63 65 67 62 72 154 170 119 165 145 170 150 145 175 142 225 118 190 104 142 114 150 145 160 20.32 24.39 19.5 23.01 22.04 25.1 24.96 21.04 25.84 24.37 33.22 28.45 25.77 20.31 25.15 18.97 23.49 26.52 21.7 86 77 77 67 70 72 70 100 85 87 88 75 81 71 61 65 67 75 79 126 106 108 110 88 96 86 120 110 99 126 115 96 102 87 85 80 106 95 40 29 31 43 18 24 16 20 25 12 38 40 15 31 26 20 13 31 16 Online STA 282QR Activity 2 (Ch11,14) Part I: For Chapter 11 NAME: ______________________________________________________________________ Problem 1. Identify each of the following problems as a matched or independent problem: 1.a) In the Pulse Rate activity, we compute the pulse rate change, Ratechange = After - Before. Is the Ratechange for female group independent of the rate change for male group? 1.b) In the Distance activity, are the samples Distance for domestic students and the sample Distance for international students independent or matched samples? 1.c) In a Pulse Rate activity, are 'Before Exercise Pulse Rate' and 'After Exercise Pulse Rate' independent or matched samples? 1.d) In the Hand size activity, are the sample heights for female group and sample heights for male group independent or matched? Problem 2. For the Raisin activity, you were asked to make your 'guess' and then count the number of raisins in a Oz box of raisin. 2.a) Are the samples of Guesses and of Actual Counts per box independent or matched samples? Explain. 2.b) We'd like to know if the average guess is significantly lower than the actual average number of raisins per box at a significance level of = 5%. The data set act14_MatchSample_Rasin(n=150).xlsx on BB contains results from 150 boxes. Download the data and perform analyses of the data. Based on this data, answer the following questions: The following is the dot plot for Guess and Actual (numbers) on the same graph. Dotplot of Guess, Actual Guess Actual 12 18 24 30 36 42 48 54 Each symbol represents up to 2 observations. Comment on the shape of the distributions. ______ Observe the difference between Guess counts and Actual counts in terms of: 1 i) Average number of raisins (which is larger)? ii) Variation of the distribution (which has more variation)? iii) Shape of the distributions: Guess count is ___________. Actual count is _____________. 2.c) Now, conduct a hypothesis test to test if the average guess is significantly lower than the actual average number of raisins per box using [NOTE: From (a), we know this is a PAIRED (or MATCHED)- sample problem. Use StatCrunch to conduct the hypothesis test problem. Let 1 be the population average of Guess count, and 2 be the population average of Actual count. i) Set up the hypotheses - H0: H 1: Is this a right-side, two-side or left-side test? _______ For paired samples, we will use PAIRED t-test, regardless of the sample size. ii) Use StatCrunch to conduct a hypothesis test to see if the average guess is significantly lower than the actual average number of raisins per box using [StatCrunch - load the data set, Go to T Stats, Paired, select Sample 1, sample 2, check 'Hypothesis test for D =', Enter Ho value, in this case it is Ho : D =choose the type of test (two-side, rightside or left side). Compute.] Copy and paste the output table here. iii) Use the output to make a decision (NOTE: use p-value). iv) What is your conclusion in terms of the context of the problem? Problem 3. In the Pulse Rate activity, students are asked to first measure their pulse rate per minute, and measure it again after exercising for one minute. Are the samples 'BMI' for female group and for male group independent or matched samples? Why? ____ 3.a) Our purpose is to see if the average BMI for Female is significantly different from the average BMI for Male. The data from130 students are recorded in the file Act14_IndepSample_ Exercise(n=130)Chap11.xlsx. Based on this data, conduct a Histogram of BMI hypothesis test to test if the average BMI for Female is significantly different from the average BMI for Male using 15 female 25 20 25 30 35 40 male Frequency 20 The histograms of BMI for Female and Male are shown on left. 15 10 the 5 0 15 20 25 30 35 40 BMI Panel variable: Gender 2 Observe the difference between Female and Male in terms of: i) Average BMI (which is larger): ___ ii) Variation of the distribution (which has more variation): ___ iii) Shape of the distributions - Female BMI: ______; Male BMI:______ [NOTE: From (a), we know this is an INDEPENDENT sample problem. ] Let 1 be the population average of Female BMI, and 2 be the population average of Male BMI. i) Set up the hypotheses - H0: H 1: Is this a right-side, two-side or left-side test? ______ For independent sample tests, we will use two-sample t-test, regardless of sample size. ii) Use StatCrunch to perform a hypothesis testing to see if the average BMI for Female is significantly different from the average BMI for Male using StatCrunch - Stat, T Stats, Two sample, With Data, enter Sample 1, Sample 2, Check 'Calculation options' Pool Variance, Check 'Hypothesis test for ' , Enter Ho value, in this case, it is 0, choose the type of test (Two-side, right or left side test), Compute.] Copy and paste output here. Copy and paste necessary output here. iii) Use the output to make a decision (NOTE: use p-value). iv) What is your conclusion in terms of the context of the problem? Problem 4. In the Pulse Rate activity, students are asked to first measure their pulse rate per minute, and measure it again after exercising for one minute. 4.a)Are the samples Before Exercise Pulse Rate and After Exercise Pulse Rate independent or matched samples? Why? ___ Our purpose is to see if the average pulse rate change (from Before exercise to After exercise) significantly increased using The data from130 students are recorded in the file Act14_IndepSample_ Exercise(n=130)Chap11.xlsx. Based on this data, conduct a hypothesis test to see if there is a significant increase in the average pulse rate (from Before Exercise to After Exercise) using The dot plots of Pulse Rates for Before and After Exercise are show below. 3 Dotplot of BEPL, AEPL BEPL AEPL 48 64 80 96 112 128 144 Observe the difference in pulse rate between Before and After exercise in terms of: i) Average Pulse Rate (which is larger): ___ ii) Variation of the distribution (which has more variation): ___ iii) Shape of the distributions - Before Exercise:________; After Exercise:_______ [NOTE: From (a), we know this is an PAIRED (or MATCHED) sample problem. ] Let's use 1 be the population average before -exercise pulse rate, and 2 be population average after-exercise pulse rate. i) Set up the hypotheses - H0: H 1: Is this a right-side, two-side or left-side test: _____ For paired sample tests, we will use PAIRED t-test, regardless of the sample size. ii) Use StatCrunch to conduct a hypothesis test to see if the average pulse rate has changed significantly increased after exercising using [Use StatCrunch to perform paired t-test.] Copy and paste the output here. iii) Use the output to make a decision (NOTE: use p-value). iv) What is your conclusion in terms of the context of the problem? 4 Part II: Regression Inference for Chapter 14 (Section 14.1) This activity re-enforces the concepts in simple linear regression model, in which there is only one explanatory X variable. Recall the one-minute exercise activity. In this activity, you will analyze the data using a simple linear regression model. Whether BMI is a significant explanatory variable/predictor of the increase in the pulse rate will be investigated. Data set: Act15_Reg_Inference_Exercise(n=110)Chap14.xlsx 1. Conduct a descriptive summary for variables Ratechange and BMI Variable Ratechange BMI 2. N Mean Standard Dev SE(Mean) Median Use StatCrunch to obtain the histogram and QQ Plot to check if the Ratechange may be normally distributed. Copy and paste both plots here. Base on the plots, do you think the distribution of Ratechange is approximately normal? ___ 3. Conduct a simple linear regression analysis and answer the following questions. [StatCrunch - Stat, Regression, Simple linear, select X and Y variables, Check Hypothesis tests. Using the default choices, Choose the graphs: Fitted line plot, Residual index plot, Histogram of residuals, QQ plot of residuals, and Predicted values Vs. residuals for the purpose of checking if the model is an adequate model (recall we did this in Chapter 4), Rows per page: 2, columns per page:3 , compute.] Copy and paste both the output and the graphs here. 3.a) What is the estimated linear regression equation? 3.b) Use the estimated regression line to predict the rate change for a BMI value of 23. ____ 3.c) Use the results in the Parameter Estimate table to conduct a t-test to see if the BMI is a significant predictor for Ratechnage. Hint: set up H0 and H1 first, and use the p-value approach to test if the slope is significantly different from 0.] 3.d) What is the R-square value? Explain or interpret this R-square value. 5