weekly exercise (hours)\tHeart Rate at rest 16\t55 2\t76 3\t78 17\t46 19\t76 3\t68 19\t61 12\t68 15\t48 2\t71 4\t72 2\t81 10\t64 9\t61 0\t73 0\t84 5\t72 16\t58 0\t77 19\t54 4\t79 8\t73 6\t85 17\t57 2\t75 7\t85 13\t73 3\t75 8\t84 6\t52 5\t60 18\t69 1\t66 19\t90 19\t64 5\t65 0\t74 2\t55 18\t67 2\t78 0\t71 18\t76 11\t76 13\t84 0\t91 The max grade for this lab is 110 but the scale is still 100 points. The 10 points are extra credit. The following video might be helpful: Histograms 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 In what follows, use any of the following tests/procedures: Regression, multiple regression, confidence intervals, onesided t-test or two-sided t-test. All the procedures should be done with a 5% P-value or a 95% confidence interval. Upload the data HeartRate_Exercise. These data are based on 45 randomly chosen high school students. Set-up: It is believed that high school students who do not exercise have a heart rate (at rest) above 70. Given the data your job is to confirm or disprove this belief. 1. What test did you perform? a. One-sided t-test b. Two-sided t-test c. Regression d. Confidence interval 2. What is the P-value/margin of error? a. 1.56075E-45 b. 3.1215E-45 c. 6.149555 d. 8.065421 e. None of these 3. What is the Statistical interpretation? a. Since the P-value is very small, we are confident that the average heart rate is above 70. b. Since the P-value is very small, we are very confident that the averages are different. c. Since the P-value is very small, we are confident that the slope of regression line is not zero. d. We are 95% certain that the confidence interval is [70.268, 86.399]. e. None of these 4. What is the conclusion? a. Yes, I am confident that the above assertion is correct. b. No, we cannot claim that the above assertion is correct. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 In what follows use any of the following tests: Regression, Multiple Regression, one- sided t-test, or two- sided t-test. All conclusions should be based on a 5% P-value threshold. Choose the best fitting answer. Upload the data HeartRate_Exercise. These data are based on 45 randomly chosen high school students. Set-up: Is it reasonable to claim that students who exercise more have a lower heart rate at rest? Given the data your job is to confirm or disprove this claim. 5. What test did you perform? a. One-sided t-test b. Two-sided t-test c. Regression d. Confidence interval 6. What is the P-value/margin of error? a. 1.56075E-45 b. 3.1215E-45 c. 6.149555 d. 0.014702 e. None of these 7. What is the Statistical interpretation? a. Since the P-value is very small, we are confident that the average heart rate is above 70. b. Since the P-value is very small, we are very confident that the averages are different. c. Since the P-value is very small, we are confident that the slope of regression line is not zero. d. We are 95% certain that the confidence interval is [72.18, 84.48]. e. None of these 8. What is the conclusion? a. Yes, I am confident that the above assertion is correct. b. No, we cannot claim that the above assertion is correct. Task 1: Confidence IntervalsIn what follows use any of the following tests: Regression, Multiple Regression, one- sided ttest, or two- sided t-test. All conclusions should be based on 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a 5% P-value threshold. Choose the best fitting answer. Upload the data HeartRate_Exercise. These data are based on 45 randomly chosen high school students. Set-up: Is it reasonable to claim that students who do not exercise or exercise less than 10 hours a week have a higher average heart rate at rest than those who exercise 10 hours or more a week? Given the data your job is to confirm or disprove this claim. 9. What test did you perform? a. One-sided t-test b. Two-sided t-test c. Regression d. Confidence interval 10. What is the P-value/margin of error? a. 7.064974 b. 0.089476 c. 0.016303 d. 0.032605 e. None of these 11. What is the Statistical interpretation? a. Since the P-value is very small, the test is conclusive. b. Since the P-value is very small, we are very confident that the averages are different. c. Since the P-value is very large, the test is inconclusive d. We are 95% certain that the confidence interval is [58.82, 72.95]. e. None of these 12. What is the conclusion? a. Yes, I am confident that the above assertion is correct. b. No, we cannot claim that the above assertion is correct. Task 2 Using the Random Generator (procedure \"Data\"\"Data Analysis\" \"Random Number Generating\") create 5000 random numbers with specifications: Number of variables = 1; Number of Random Numbers = 5000; Distribution = 0 0 0 0 0 Normal; Mean = 100; Standard Deviation = 15. Leave the Seed box empty! Click OK and a 5000 long number column will appear. Make bins by typing 50, 60,...., 150 (see picture below): 0 Go to the Histogram box by clicking on \"Data\" \"Data Analysis\" \"Histogram\". Highlight the 5000 data points under the Input range box and highlight the bins under Bin Range (Careful with Labels: if you choose to highlight labels, then you must activate the Label box). Click OK and the following Table should appear: 0 0 0 Highlight all the outputs (as seen on the picture) and create a chart (Use Bar Chart option under Insert tab): 0 0 In the task that follows, use these charts as a guide to distinguish. Use the charts labeled: Bell Shape, Double Bell shape and Skewed Upload the Tornadoes data, and make the histogram using (highlighting) all 12 columns for months and tornado numbers. Do not use annual tornadoes and do not use tornado deaths. (Be careful how you choose the bins). Answer the following questions for Assessment: 13. The histogram chart should resemble the shape 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 presented as: a. Bell shape b. Double-bell shape c. Skewed 14. Compute the Median, StDev, and Average for this whole data set (i.e., all 12 columns for month and tornado numbers not tornado deaths). Choose the correct statement. a. Average < Median < StDev b. StDev < Median < Average c. StDev < Average < Median d. Median < Average < StDev Upload the Weight data, make the histogram (careful how you choose the bins) and answer the following questions: 15. The histogram chart should resemble the shape as: a. Bell shape b. Double-bell shape c. Skewed 16. Compute the Median, StDev, and Average for this whole data set. Choose the correct statement. a. Average < Median < StDev b. StDev < Median < Average c. StDev < Average < Median d. Median < Average < StDev Tutorial A Open the PreLaw_Nursing data. Set-up: Do Nursing and PreLaw majors have different salaries? Given the data, answer this question. HINT: Read Lecture 24. 17. What would be the correct Null-Hypothesis? a. Nursing and Pre-Law majors have different salaries. b. The population averages are equal. c. Nursing salaries and Pre-law salaries are related. d. Nursing salaries and Pre-law salaries are not related. 18. The P-value is 0.0006, what can be statistically concluded? a. We reject the Null Hypothesis. b. We accept the Null Hypothesis. 0 0 0 0 0 0 0 0 0 c. The test is inconclusive. d. None of the above. 19. What would be an appropriate comment? a. We cannot conclude that Nursing and Pre-Law majors have different salaries. b. We are confident that Nursing and Pre-Law majors have different salaries. c. We are confident that Nursing salaries influence the Pre-Law salaries. d. None of the above. 20. Which of the following is NOT a rule of thumb? a. The Null-Hypothesis is always stated with an \"equal\" sign. Either: The (population) averages are equal, or The slope of the regression line is equal zero. b. If the P-value is good (typically below 5%), we reject the Null-Hypothesis. c. If the P-value is bad (typically above 5%), we accept the Null-Hypothesis. d. Mathematically, we can never state: We accept the Null-Hypothesis. PreLaw\tNursing 46\t38 33\t42 33\t42 41\t41 31\t42 41\t43 41\t43 34\t51 44\t41 40\t37 39\t45 32\t43 29\t39 36\t44 43\t41 31\t46 34\t35 39\t47 42\t48 34\t47 39\t38 42\t38 38\t39 45\t44 39\t45 Tornadoes and Deaths by Year and Month (1950-1994) Year\tTotal Tornadoes\tTornadoes by Month Total Deaths\tDeaths by Month Jan\tFeb\tMar\tApr\tMay\tJune\tJuly\tAug\tSept\tOct\tNov\tDec Jan\tFeb\tMar\tApr\tMay\tJune\tJuly\tAug\tSept\tOct\tNov\tDec 1950\t201\t7\t20\t21\t15\t61\t28\t23\t13\t3\t2\t4\t4\t70\t1\t45\t1\t12\t2\t6\t0\t0\t0\t0\t0\t3 1951\t260\t2\t10\t6\t26\t57\t76\t23\t27\t9\t2\t12\t10\t34\t0\t1\t0\t2\t7\t9\t5\t0\t8\t0\t1\t1 1952\t240\t12\t27\t43\t37\t34\t34\t27\t16\t1\t0\t6\t3\t230\t0\t10\t209\t4\t2\t2\t2\t1\t0\t0\t0\t0 1953\t422\t14\t16\t40\t47\t94\t111\t32\t24\t5\t6\t12\t21\t519\t0\t3\t24\t36\t163\t244\t0\t0\t0\t0\t0\t49 1954\t550\t2\t17\t62\t113\t101\t107\t45\t49\t21\t14\t2\t17\t36\t0\t2\t10\t2\t9\t5\t0\t1\t3\t2\t0\t2 1955\t593\t3\t4\t43\t99\t148\t153\t49\t33\t15\t23\t20\t3\t129\t0\t0\t5\t7\t106\t2\t5\t0\t2\t1\t1\t0 1956\t504\t2\t47\t31\t85\t79\t65\t92\t42\t16\t29\t7\t9\t83\t0\t8\t1\t67\t4\t0\t1\t2\t0\t0\t0\t0 1957\t858\t17\t5\t38\t216\t228\t147\t55\t20\t17\t18\t59\t38\t193\t13\t0\t1\t30\t87\t14\t0\t0\t2\t2\t25\t19 1958\t564\t11\t20\t15\t76\t68\t128\t121\t46\t24\t9\t45\t1\t67\t0\t13\t0\t4\t0\t43\t1\t1\t1\t4\t0\t0 1959\t604\t16\t20\t43\t30\t226\t73\t63\t38\t58\t24\t11\t2\t58\t3\t21\t9\t1\t8\t2\t0\t0\t14\t0\t0\t0 1960\t616\t9\t28\t28\t70\t201\t125\t42\t48\t21\t18\t25\t1\t46\t0\t0\t0\t7\t34\t3\t0\t1\t0\t1\t0\t0 1961\t697\t1\t31\t124\t74\t137\t107\t77\t27\t53\t14\t36\t16\t52\t0\t0\t7\t4\t23\t2\t0\t0\t15\t0\t1\t0 1962\t657\t12\t25\t37\t41\t200\t171\t78\t51\t24\t11\t5\t2\t30\t1\t0\t17\t2\t4\t0\t0\t6\t0\t0\t0\t0 1963\t463\t15\t6\t48\t84\t71\t90\t62\t26\t33\t13\t15\t0\t31\t1\t0\t8\t16\t1\t0\t0\t2\t3\t0\t0\t0 1964\t704\t14\t2\t36\t157\t134\t137\t63\t79\t25\t22\t17\t18\t73\t10\t0\t6\t15\t16\t0\t0\t2\t0\t22\t0\t2 1965\t897\t21\t32\t34\t123\t273\t147\t85\t61\t64\t16\t34\t7\t301\t0\t0\t2\t268\t17\t7\t0\t1\t0\t1\t5\t0 1966\t585\t1\t28\t12\t80\t98\t126\t100\t58\t22\t29\t20\t11\t98\t0\t0\t58\t12\t0\t19\t3\t0\t0\t6\t0\t0 1967\t926\t39\t8\t42\t149\t116\t210\t90\t28\t139\t36\t8\t61\t114\t7\t0\t3\t73\t3\t6\t1\t2\t5\t4\t0\t10 1968\t660\t5\t7\t28\t102\t145\t136\t56\t66\t25\t14\t44\t32\t131\t0\t0\t0\t40\t72\t11\t2\t2\t0\t0\t3\t1 1969\t608\t3\t5\t8\t68\t145\t137\t98\t70\t20\t26\t5\t23\t66\t32\t0\t1\t2\t4\t7\t0\t19\t0\t0\t0\t1 1970\t654\t9\t16\t25\t117\t88\t134\t82\t55\t54\t50\t10\t14\t73\t0\t0\t2\t30\t26\t6\t3\t0\t0\t6\t0\t0 1971\t889\t19\t83\t40\t75\t166\t199\t100\t50\t47\t38\t16\t56\t159\t1\t134\t2\t11\t7\t1\t1\t0\t0\t0\t0\t2 1972\t741\t33\t7\t69\t96\t140\t114\t115\t59\t49\t34\t17\t8\t27\t5\t0\t0\t16\t0\t2\t0\t2\t0\t0\t2\t0 1973\t1102\t33\t10\t80\t150\t250\t224\t80\t51\t69\t25\t81\t49\t89\t1\t0\t17\t10\t35\t3\t1\t4\t3\t0\t12\t3 1974\t945\t24\t23\t36\t267\t144\t194\t59\t107\t25\t45\t13\t8\t366\t2\t0\t1\t317\t10\t31\t0\t0\t0\t5\t0\t0 1975\t919\t52\t45\t84\t108\t188\t196\t79\t60\t34\t12\t39\t22\t60\t12\t7\t12\t13\t5\t6\t2\t2\t0\t0\t0\t1 1976\t834\t12\t36\t180\t113\t155\t169\t84\t38\t35\t11\t0\t1\t44\t0\t5\t21\t1\t8\t3\t2\t1\t3\t0\t0\t0 1977\t852\t5\t17\t64\t88\t228\t132\t99\t82\t65\t25\t24\t23\t43\t0\t2\t0\t26\t4\t0\t1\t6\t1\t1\t0\t2 1978\t789\t23\t7\t17\t107\t213\t148\t143\t65\t20\t7\t9\t30\t53\t2\t0\t0\t4\t7\t17\t11\t1\t6\t0\t0\t5 1979\t855\t16\t4\t53\t123\t112\t150\t132\t126\t69\t47\t21\t2\t84\t0\t0\t1\t58\t2\t8\t1\t5\t2\t7\t0\t0 1980\t866\t5\t11\t41\t137\t203\t217\t95\t73\t37\t43\t3\t1\t28\t0\t0\t2\t4\t8\t7\t5\t0\t1\t1\t0\t0 1981\t782\t2\t25\t33\t84\t187\t223\t98\t64\t26\t32\t7\t1\t24\t0\t2\t1\t13\t0\t8\t0\t0\t0\t0\t0\t0 1982\t1047\t18\t3\t60\t150\t329\t196\t95\t34\t38\t9\t19\t96\t64\t1\t0\t6\t30\t14\t4\t0\t0\t2\t0\t0\t7 1983\t931\t13\t41\t71\t65\t249\t178\t99\t76\t19\t13\t49\t58\t34\t2\t1\t0\t6\t14\t2\t4\t0\t0\t0\t0\t5 1984\t907\t1\t27\t73\t176\t169\t242\t72\t47\t17\t49\t30\t4\t122\t0\t0\t64\t33\t6\t14\t0\t0\t0\t4\t1\t0 1985\t684\t2\t7\t38\t134\t182\t82\t51\t108\t40\t18\t19\t3\t94\t0\t0\t2\t5\t78\t3\t0\t3\t0\t0\t3\t0 1986\t765\t0\t30\t76\t84\t173\t134\t88\t67\t65\t26\t17\t5\t15\t0\t2\t6\t2\t1\t0\t3\t1\t0\t0\t0\t0 1987\t656\t6\t19\t38\t20\t126\t132\t163\t63\t19\t1\t55\t14\t59\t0\t6\t1\t1\t31\t2\t0\t1\t0\t0\t11\t6 1988\t702\t17\t4\t28\t58\t132\t63\t103\t61\t76\t19\t121\t20\t32\t5\t0\t1\t4\t3\t0\t0\t3\t1\t0\t14\t1 1989\t856\t14\t18\t43\t82\t231\t252\t59\t36\t31\t30\t57\t3\t50\t0\t0\t1\t0\t9\t5\t0\t0\t0\t4\t31\t0 1990\t1133\t11\t57\t86\t108\t243\t329\t106\t60\t45\t35\t18\t35\t53\t0\t1\t3\t0\t5\t11\t0\t29\t0\t2\t0\t2 1991\t1132\t29\t11\t157\t204\t335\t216\t64\t46\t26\t21\t20\t3\t39\t1\t0\t13\t21\t0\t1\t1\t0\t0\t0\t2\t0 1992\t1297\t15\t29\t55\t53\t137\t399\t213\t115\t81\t34\t146\t20\t39\t0\t0\t5\t0\t0\t1\t0\t3\t0\t4\t26\t0 1993\t1173\t17\t34\t48\t85\t177\t313\t242\t112\t65\t55\t19\t6\t33\t0\t3\t5\t10\t2\t1\t0\t6\t2\t4\t0\t0 1994\t1082\t13\t9\t58\t205\t161\t234\t155\t120\t30\t51\t42\t4\t69\t0\t0\t40\t12\t0\t3\t3\t4\t0\t0\t7\t0