Chapter 11 Assignment Name Description of the Data: Results of a randomized comparative experiment to investigate the effect of calcium on blood pressure in African-American men. A treatment group of 10 men received a calcium supplement for 12 weeks, and a control group of 11 men received a placebo during the same period. All subjects had their blood pressure tested before and after the 12-week period. (See the Excel File \"Chapter 11 Dataset\" to complete the questions below.) Variable Names: 1. Treatment: Whether subject received calcium or placebo 2. Begin: seated systolic blood pressure before treatment 3. End: seated systolic blood pressure after treatment 4. Decrease: Decrease in blood pressure (Begin - End) Research Question: Does taking a calcium supplement affect blood pressure in AfricanAmerican men? 1. What type of t-test will we perform? 2. What are the independent and dependent variables? Independent variable: Dependent variable: Now, let's check the assumptions for performing a t-test. a) Sampling distribution should be normal (i.e. the dependent variable should be normally distributed) At the bottom of the Excel file, click on \"Sheet 2.\" Here, you'll see I have created a normality plot and a histogram for you to use to make your decision regarding the normality of the data. In addition, you should consider the skewness and kurtosis values described in Chapter 8. To find these, click the DATA tab then choose Data Analysis. Click \"Descriptive Statistics.\" Click the box next to input range, highlight your dependent variables. If you included the label, click the box next to Labels in first row. Click the circle next to output range. In the box, type F2. Click the box next to Summary statistics. Hit OK. 3. Skewness: Kurtosis: 4. Using the above information does it appear the data follow a normal distribution? Explain your answer. b) Data should be measured at least an interval level (i.e. continuous measurement) 5. Are the data a continuous measurement? c) Variances in each group should be about the same We're going to use an F-Test to test equality of variances for each of our groups. At the bottom of the file, click \"Sheet 3.\" Click the DATA tab then choose Data Analysis. Choose \"F-Test TwoSample for Variances.\" Click the box next to Variable 1 Range. Click column A. Click the box next to Variable 2 Range. Click column B. Check the box next to Labels. Click the box next to Output Range and type D2. Hit OK. 6. Report the p-value and your conclusion about the equality of variances. p-value: Conclusion : d) Measurements should be independent 7. Are the measurement independent? Explain your answer. 8. Identify the null and alternative hypothesis. H0: H1: Now, let's perform our t-test. At the bottom of the Excel file, click \"Sheet 3.\" Click the DATA tab then Data Analysis. Choose \"t-Test: Two-Sample Assuming Equal Variances.\" Click the box next to \"Variable 1 Range.\" Click on column A. In the box next to \"Variable 2 Range,\" click on column B. For \"Hypothesized Mean Difference,\" type 0. Check the box next to Labels. In the box next to \"Output Range,\" type A15. 9. Identify the appropriate test statistic and p-value. Test statistic: p-value: 10. What do you conclude about the mean difference in blood pressure for those given a calcium supplement? Treatment Calcium Calcium Calcium Calcium Calcium Calcium Calcium Calcium Calcium Calcium Placebo Placebo Placebo Placebo Placebo Placebo Placebo Placebo Placebo Placebo Placebo Begin End 107 110 123 129 112 111 107 112 136 102 123 109 112 102 98 114 119 112 110 117 130 Decrease 100 114 105 112 115 116 106 102 125 104 124 97 113 105 95 119 114 114 121 118 133 7 -4 18 17 -3 -5 1 10 11 -2 -1 12 -1 -3 3 -5 5 2 -11 -1 -3 Difference Expected z i -11 -1.88951 -5 -1.4292194 -5 -1.1575228 -4 -0.9518433 -3 -0.7801644 -3 -0.6289042 -3 -0.4908544 -2 -0.3616052 -1 -0.2381501 -1 -0.1182339 -1 0 1 0.11823387 2 0.23815006 3 0.36160523 5 0.49085443 7 0.62890422 10 0.78016439 11 0.95184328 12 1.15752281 17 1.42921942 18 1.88950996 f 1 0.029412 2 0.076471 3 0.123529 4 0.170588 5 0.217647 6 0.264706 7 0.311765 8 0.358824 9 0.405882 10 0.452941 11 0.5 12 0.547059 13 0.594118 -10 -15 14 0.641176 15 0.688235 16 0.735294 17 0.782353 18 0.829412 19 0.876471 20 0.923529 21 0.970588 Normal Probability Plot 2.5 2 1.5 1 0.5 0 -5 0 5 10 15 20 -0.5 -1 -1.5 -2 -2.5 Histogram Bins -10 -5 0 5 10 15 20 9 8 7 6 5 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 -0.75 -0.7 -0.65 -0.6 -0.55 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 0.004199Frequency 0.005574 0.007275 0.009336 0.01178 0.014614 0.017825 0.021378 0.025208 0.029225 0.033314 0.037338 0.041146 0.044581 0.047492 0.049744 0.051229 0.051873 0.051644 0.050553 0.048654 0.046041 0.042837 0.039188 0.035247 0.031171 0.027104 0.023172 0.019478 0.016098 0.013081 0.010451 0.00821 0.006341 0.004816 0.003596 0.00264 0.001906 0.001352 0.000944 0.000647 4 3 2 1 0 Bin Frequency -10 1 -5 2 0 8 5 4 10 2 15 2 20 2 last Point Mean E(x^2f) E(xf)^2 E(f) Variance StDev 20 2.238095 1700 8100 21 1314.286 7.687033 -10 -5 0 5 10 15 20 Difference Calcium Difference Placebo 7 -4 18 17 -3 -5 1 10 11 -2 -1 12 -1 -3 3 -5 5 2 -11 -1 -3