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\f44 F 23.2 2001 1980 728 700 43 75 886 1000 45 F 14 18 19.5 1648 1746 782 700 69 75 914 46 F 1000 11 18 21.8 1751 2000 366 700 25 65 487 47 F 1300 10 22.6 15 1663 2053 793 700 46 75 1069 1000 48 F 15 22.7 18 2036 2092 862 700 85 60 949 49 F 1000 16 18 23.5 1904 2114 1148 700 64 75 1179 1000 50 F 20 23.4 18 2238 2075 670 700 48 75 1053 51 F 1000 15 22.5 18 1796 2120 618 700 155 75 808 52 F 1000 23 18 23.2 1801 1734 512 485 18 56 1180 53 F 1300 9 23.5 15 1408 2000 932 1666 177 60 670 54 F 1000 23 21 18 1647 1664 787 700 11 65 1538 1300 55 F 10 15 20.7 2435 2400 602 700 55 65 585 1300 56 F 11 15 23.5 1893 2114 321 700 35 75 57 F 1024 1000 16 19.6 1353 18 1872 485 700 90 60 697 1000 10 58 M 18 21.1 3267 2649 2008 900 208 90 1690 1000 59 M 31 8 21 2957 2593 1352 900 213 90 1467 60 M 1000 20.7 15 8 3259 2606 652 900 117 90 1706 1000 61 M 19 8 21.1 3453 2677 541 900 235 90 1373 1000 62 M 27 8 25.8 1368 2709 778 900 43 90 1237 63 M 1000 23 18.9 8 1554 2666 356 900 44 90 532 64 M 1000 16 8 18.1 1490 2092 548 700 82 60 508 1000 21 65 M 18 24.2 3484 3428 1000 900 106 75 1608 66 M 1300 28 19 11 2738 2494 839 900 43 90 1343 67 M 1000 22.1 12 8 1647 2000 205 900 38 90 460 1000 11 68 M 8 25.8 1658 2238 679 700 43 75 735 69 M 1000 19 24.4 18 2349 2764 348 900 23 90 1238 1000 70 M 16 8 23.6 1977 2433 621 900 47 90 790 1000 71 M 14 8 22.4 2491 2577 562 900 39 75 1163 1300 15 111. Conceptual, computing the p-value requires that our original summary measurement, i.e. the average value for the difference column, be compared against repeated outcomes under the situation of no difference between these two groups. Which simulation version, i.e. Version A or Version B, should be used to compute the p-value for this problem? Provide a rationale for your selection. (3 pts) Version A | Version B Original Data Avg = -166 Version A Simulation -300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300 Difference = Actual - DRI Version B Simulation -300 -250 -200 -150 -100 -50 50 100 150 200 250 300 Difference = Actual - DRI Provide a rationale for your choice. 2. Run an appropriate paired t-test that would answer the following research question. Research Question: Do statistical differences exist, on average, between the actual and daily recommended intake of Calcium for college students at Winona State University? The goal of this study is to compare the Actual Intake of Calcium to the Daily Recommended Intake (DRI) of Calcium. A statistician would immediately calculate the differences between Actual and DRI and complete the analysis using these differences. Suppose instead your friend decides to conduct their analysis by simply comparing the Actual column to the DRI column without computing the differences. F Gender BMI Energy Actual Energy DRI Calcium Actual Calcium DRI Calcium Actual 1 F 22.5 2123 1758 761 1300 4Summary Statistics 2 F 19.7 2436 1882 928 1000 Mean 947.9 3 F 23.1 2614 1924 783 1000 Std Dev 406.1 AF 1.5 2879 2235 1646 1000 N 71 Calcium DRI 4Summary Statistics Mean 1114 Std Dev 146.7 N 71Research Question: Do statistical differences exist, on average, between the actual and daily recommended intake of Calcium for college students at Winona State University? Step 1: Obtain null and alternative hypothesis. Ho : On average, no difference exists between actual and daily recommended intake of Calcium for WSU Students HA : On average, a difference exists between actual and daily recommended intake of Calcium for WSU Students or equivalently, H H Difference = 0 HAHDifference * 0 Step 2: Use a 5% an error rate which implies conclusions will be made with 95% confidence. Step 3: Complete a paired t-test is JMP. (3 pts) Provide a screen-shot of your JMP output. Step 4: Obtain the p-value and make decision (3 pts) P-Value: N Research Question: Do statistical differences exist, on average, between the actual and daily recommended intake of Calcium for college students at Winona State University? The goal of this study is to compare the Actual Intake of Calcium to the Daily Recommended Intake (DRI) of Calcium. A statistician would immediately calculate the differences between Actual and DRI and complete the analysis using these differences. Suppose instead your friend decides to conduct their analysis by simply comparing the Actual column to the DRI column without computing the differences. F Gender BMI Energy Actual Energy DRI Calcium Actual Calcium DRI 4Calcium Actual 1 F 22.5 2123 1758 76 1300 4Summary Statistics 2 F 19.7 2436 1882 928 1000 Mean 947.9 23.1 2614 1924 783 1000 Std Dev 406.1 21.5 2879 2235 1646 1000 N 71 Calcium DRI 4Summary Statistics Mean 1114 Std Dev 146.7 N 71The Decision Rule: If the p-value is less than the error rate, then the data is said to support the research question. . Data provided enough evidence for research question (reject H.) Data does not provided enough evidence for research question (fail to reject H.) Step 5: Write a final statement using layman's language. (4 pts) Consider the following summary statistics output that is provided by JMP. 4Summary Statistics Mean -166 Std Dev 418.7 Std Err Mean 49.69 Upper 95% Mean -67.1 Lower 95% Mean -265 N 71 3. Provide an interpretation of the 95% Confidence Interval. The 95% confidence interval is -265.0 up to -67.1. (3 pts) Research Question: Do statistical differences exist, on average, between the actual and daily recommended intake of Calcium for college students at Winona State University? The goal of this study is to compare the Actual Intake of Calcium to the Daily Recommended Intake (DRI) of Calcium. A statistician would immediately calculate the differences between Actual and DRI and complete the analysis using these differences. Suppose instead your friend decides to conduct their analysis by simply comparing the Actual column to the DRI column without computing the differences. F Gender BMI Energy Actual Energy DRI Calcium Actual Calcium DRI 4Calcium Actual 1 F 22.5 2123 1758 761 1300 4Summary Statistics 2 F 19.7 2436 1882 928 1000 Mean 947.9 3 F 23.1 2614 1924 783 1000 Std Dev 406.1 21.5 2879 2735 1646 1000 N 71 4Calcium DRI 4Summary Statistics Mean 1114 Std Dev 146.7 N 714. One last problem, what is the purpose of Std Err Mean? Why might a statistician care about this value? Briefly discuss. (2 pts) A Research Question: Do statistical differences exist, on average, between the actual and daily recommended intake of Calcium for college students at Winona State University? The goal of this study is to compare the Actual Intake of Calcium to the Daily Recommended Intake (DRI) of Calcium. A statistician would immediately calculate the differences between Actual and DRI and complete the analysis using these differences. Suppose instead your friend decides to conduct their analysis by simply comparing the Actual column to the DRI column without computing the differences. F Gender BMI Energy Actual Energy DRI Calcium Actual Calcium DR 4Calcium Actual 1 F 22.5 2123 1758 761 1300 40Summary Statistics 2 F 19.7 2436 1882 928 1000 Mean 947.9 3 F 23.1 2614 1924 783 1000 Std Dev 406.1 AF 21.5 2879 2235 1646 1000 N 71 4Calcium DRI Summary Statistics Mean 1114 Std Dev 146.7
