1. BST 322 Week 2 Assignment What is the probability of rolling a four in the gambling dice game of craps (given two six sided dice)? What is the probability that a player can roll a four 3 times in a row (assume that rolling the dice each time does not affect the outcome of the next roll)? 8.3 probability of rolling a 4. 2. 0.0578% probability of rolling a 4 three times. Population A and Population B both have a mean height of 70.0 inches with an SD of 6.0. A random sample of 30 people is picked from population A, and random sample of 50 people is selected from Population B. Which sample mean will probably yield a more accurate estimate of its population mean? Why? Population B due to the fact that they have more samples to review. A more accurate conclusion can be hypothesized compared to the 30 samples reviewed by the other researchers. 3. Suppose we obtained data on vein size after application of a nitroglycerin ointment in a sample of 50 patients. The mean vein size is found to be 8.7mm with an SD of 2.1. Using a t distribution table, what are the confidence limits for a 95% confidence interval? For a 99% confidence interval? One sample T hypothesis test: : Mean of population H0 : = 0 HA : 0 Hypothesis test results: Mean Sample Mean Std. Err. DF T-Stat P-value 8.7 0.29698485 49 29.294424 <0.0001 One sample T confidence interval: : Mean of population 95% confidence interval results: Mean Sample Mean Std. Err. DF L. Limit U. Limit 8.7 0.29698485 49 8.1031866 9.2968134 The data on mean vein size is considered significant with a p value of 0.0001 The L limit and U limit shows us that the average will range from 8.10 to 9.29. One sample T confidence interval: : Mean of population 99% confidence interval results: Mean Sample Mean Std. Err. DF L. Limit U. Limit 8.7 0.29698485 49 7.9040949 9.4959051 With the given confidence interval result of 99% confidence we see that the average mean vein size will range from 7.90 to 9.49. 4. In a pilot study evaluating the use of a new drug to lower resting heart rates (HR) of patients, the following data was recorded: Subject # 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 Resting HR 72 88 71 87 64 77 79 59 77 68 78 89 91 81 85 75 69 Given that the average resting HR of the general population for this study is 72, use StatCrunch to perform the appropriate t test. What is the value of t? Using an alpha of 0.05, is the t statistic significant? Why? What are the confidence limits for a 95% confidence interval here and what do they mean for this patient group? Copy and Paste your work from StatCrunch into your Word document submission. One sample T hypothesis test: : Mean of variable H0 : = 72 HA : 72 Hypothesis test results: Variable resting HR Sample Mean Std. Err. 77.058824 2.2269581 DF T-Stat 16 2.2716294 P-value 0.0373 One sample T confidence interval: : Mean of variable 95% confidence interval results: Variable resting HR Sample Mean Std. Err. 77.058824 2.2269581 DF L. Limit U. Limit 16 72.337883 81.779764 2.27 Yes because the P value is under .05 being .037 If we continue to sample we will find that 95% of the time their heart rates will be between 72.34 and 81.78 5. Write one or two sentences that could be used to report the results obtained for the t-test in Exercise 4. The null hypothesis is that the vein size will not change from the original average of 72. The alternate hypothesis is that the vein size will change from the original average of 72. The P value is significant which means we can reject the null hypothesis. 6. For which of the following situations is the independent groups t-test appropriate (if inappropriate, why?): a. The independent variable is infant birth weight at one week (normal vs high); the dependent variable is resting heart rate. Appropriate because resting heart rate does not affect birth weight. b. The independent variable is radiation treatment on throat cancer patients (after a low dose and then a high dose treatment); the dependent variable is white blood cell count. Not appropriate because the radiation treatment on throat cancer will affect the white blood cell count. c. The IV is infant birth weight (low vs normal vs high); the DV is number of days absent from school in first grade. Appropriate because birth weight had nothing to do with missing school on the first day. d. The IV is gender (male vs female); the DV is compliance vs noncompliance with a medication regimen. Appropriate because being male or female will not determine whether a child/adult will comply or not. e. The independent variable is married status (single vs married); the dependent variable is happiness measured on a scale from 1 to 50 Not appropriate because marital status reveals information about the status of their happiness on a scale of 1 -10 7. For which of the following situations is the dependent groups t-test appropriate (if not appropriate, why?) a. The IV is presence or absence of conversation directed to comatose patients (same patients with and without conversation); the DV is the patients' intracranial pressure. Not appropriate because talking does not affect intracranial pressure. b. The IV is birth type (home vs hospital); the DV is perceived functional ability of the patient 48 hours after surgery. Not appropriate because the functional ability of the patient will be the same if at home or in the hospital. c. The IV is time since incarceration (1 months vs 3 months vs 6 months); the DV is body weight. Appropriate because you can observe the same individual over and over again. d. The IV is menopausal state (pre vs post) in the same women over time; the DV is attitudes toward menopause. Appropriate because you are testing the same women over time menopause state effects the attitude towards menopause. e. The IV is nap therapy for narcoleptics (same patients before vs after treatment); the DV is the type of nap they had the following week (had unplanned vs didn't have unplanned nap). Appropriate because you are testing the same person. 8. Suppose we wanted to test the hypothesis that a control group of cancer patients (Group 1) would report higher mean pain ratings than an experimental group receiving special massage treatments (Group 2). Use the following information. Compute a t-statistic for independent groups: mean group 1 = 78.1 mean group 2 = 74.1 SD21 = 42.1 SD22 = 39.7 n1 = 25 n2 = 25 What are the degrees of freedom and the value of t ? Using =0.05 for a two-tailed test, is this t statistic significant? Show your calculations (or StatCrunch output) for full credit. 9. Write one or two sentences that could be used to report the results obtained for the t-test in Exercise 8. 10. For each of the following t values, indicate whether the t is statistically significant for a two-tailed test, at the specified alphas: a. b. t = 2.90, df = 25, = 0.01 t = 2.00, dr = 25, = 0.05 c. d. t = 5.52, df = 10, = 0.01 t = 2.02, df = 20, = 0.05 11. For each of the following situations, indicate whether ANOVA is appropriate; if not appropriate, the reason why not; and, if appropriate, the type of ANOVA that would be used (i.e., one-way, repeated measures, etc.) a. The IVs are ethnicity (Asian, White, African American, Hispanic) and gender (male vs female); the DV is serum cholesterol levels. b. The IV is smoking status - smokers vs non-smokers; the DV is health-related hardiness as measured on a 20-item scale. c. The IV is maternal breast feeding status (breastfeeds daily vs breastfeeds at least 1-3 times/week vs doesn't breastfeed); the DV is maternal bonding with infant, as measured on a 20-item self-report scale. d. The IV is treatment group for patients with drug-induced shivering (extremity wraps vs high room temp vs normal room temp without wraps) different patients used for each treatment; the DV is myocardial oxygen consumption (measured in ml O2/min per 100g of tissue). e. The IV is length of gestation (preterm vs term vs postterm) using the same multiple birth mothers over time; the DV is blood pressure 10 minutes post delivery. 12. Suppose we wanted to compare the somatic complaints (as measured on a scale known as the Physical Symptom Scale or PSS) of three groups of people: non-smokers, smokers, and people who recently quit smoking. Using the following data for PSS, do a one-way ANOVA to test the hypothesis that the population means are equal: Nonsmokers Smokers Quitters 19 31 30 28 29 22 17 22 29 20 29 29 25 28 34 Using StatCrunch, determine the means for the three groups and compute the sums of squares, degrees of freedom, and mean squares for these data. What is the value of F? Using an alpha of 0.05, is the F statistic significant? Why? Copy and Paste your work from StatCrunch into your Word document submission. 13. A new motorcycle is being developed to meet new gas mileage standards recently passed by the federal government. An engineer tested three model designs by randomly assigning the motorcycles in a blind study (the riders recorded the mileage but did not know the design of the motorcycle, only its code). The data in miles per gallon (MPG) for the three designs is listed below: X-1 45 62 50 65 62 50 50 58 B-1 55 55 54 44 52 69 58 45 Z-1 54 52 41 40 38 39 51 64 Using StatCrunch, determine the means for the three groups and compute the sums of squares, degrees of freedom, and mean squares for these data. What are the hypotheses to be tested here? What is the value of F? Using an alpha of 0.05, is the F statistic significant? Why? Copy and Paste your work from StatCrunch into your Word document submission for full credit. 14. For each of the following F values, indicate whether the F is statistically significant at the specified alpha level: a. b. c. F = 4.80, df = 4, 40 = 0.01 F = 5.02, df = 3, 60, = 0.001 F = 3.45, df = 3, 27, = 0.05 d. e. F = 1.99, df = 2, 150, = 0.05 F = 3.09, df = 2, 250, = 0.05