The paper “Effect of a Nutritional Supplement on Hair Loss in Women” (Journal of Cosmetic Dermatology [2015]: 76-82) describes an experiment to see if a dietary supplement consisting of Omega 3, Omega 6, and antioxidants could reduce hair loss in women with stage 1 hair loss. One hundred twenty women volunteered to participate in the study and were randomly assigned to either the supplement group or a control group. The women in the supplement group took the supplement for 6 months. Photos of the top of the head were taken of all the women at the beginning of the study and 6 months later at the end of the study. The two photos of each woman were evaluated by an independent expert who visually determined the change in hair density. The expert who determined the change in hair density did not know which of the women had taken the supplement.
- a. Evaluate this experimental design. Do you think this is a good design or a poor design, and why?
- b. If you were designing such a study, what, if anything, would you propose to do differently?
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Chapter 2 Solutions
Introduction To Statistics And Data Analysis
- A consumer advocacy group wanted to study whether different airline carriers differed in terms of their delayed flights. In particular, the researchers were interested in the relationship between p1, the proportion of Alpha Airlines flights that were delayed at least 15 minutes, and p2, the proportion of Beta Airlines flights that were delayed at least 15 minutes. A random sample of 1,000 Alpha flights and a separate random sample of 1,000 Beta flights found that 67 of the Alpha fights and 160 of the Beta flights were delayed at least 15 minutes. The conditions for inference were checked and verified. Does this set of samples provide strong evidence that Alpha Airlines has a smaller proportion of flights that are delayed at least 15 minutes than Beta Airlines, at the α = 0.05 significance level? Find the z-table here. A. The test statistic is z = –6.56 and the P-value ≈ 0. Since the P-value ≈ 0 < 0.05, there is not sufficient evidence that Alpha Airlines has fewer delayed…arrow_forwardA study was performed on 200 elementary school students to investigate whether regular Vitamin A supplementation was effective in preventing colds during the month of March. 100 were randomized to receive daily Vitamin A supplements during the month of March, and 100 students were randomized to a placebo group (and did not receive Vitamin A) during the same month. The number of students getting at least one cold in March was computed in the two groups, and the results are given in the following 2 X 2 table. Using a 5% level of significance determine whether there is an association between Vitamin A supplementation and prevention of Common Cold ColdNo Cold Vitamin A1585100 Placebo2575100 40160200arrow_forwardAn article from the American Journal of Public Health reports the results from a randomized study designed to evaluate the efficacy of an intervention targeted to Hispanic/Latino men who identify as gay, bi-sexual or other men who have sex with men (MSM). A representative sample of 254 such men was randomized to be in either the intervention group (n=152, with 141 ultimately participating in the study) or the control group (n=152, with 147 ulitmately participating in the study). The primary outcome under study getting tested for HIV within the six-months following group assignment (randomization) among those who had been sexually active in this same six-month follow-up period. At six months of follow-up, 141 subjects in the intervention group reported having had sex (with men and/or women) since randomization. Of these 141 men, 114 had been tested for HIV since being randomized. At six months of follow-up, 147 subjects in the control group reported having had sex (with men…arrow_forward
- A study of “adverse symptoms” in users of over-the-counter pain relief medications assigned subjects at random toone of two common pain relievers: acetaminophen and ibuprofen. In all, 650 subjects took acetaminophen, and 44experienced some adverse symptom. Of the 347 subjects who took ibuprofen, 49 had an adverse symptom. Is thisconvincing evidence that the two pain relievers differ in the proportion of people who experience an adverse symptom?arrow_forwardElizon Pharmaceuticals, Inc., announced the results of its first human trial of NPI 32101, a topical form of its skin ointment. A total of 225 patients diagnosed with skin irritations were randomly divided into three groups as part of a double-blind, placebo-controlled study to test the effectiveness of the new topical cream. The first group received a 0.5% cream, the second group received a 1.0% cream, and the third group received a placebo. Groups were treated twice daily for a 6-week period. (a)What type of experimental design is this? (b)What is the control group for this study? (c)What is the factor that is set to predetermined levels? What is the treatment? (d)What does it mean for this study to be double-blind? (e)Identify the experimental units. (f)Draw a diagram to illustrate the design.arrow_forward4) A medical researcher is interested in determining if there is a relationship between adults over 50 who exercise regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and the results are given below. Test the claim that regular exercise and low, moderate, and high blood pressure are independent. Use alpha= 0.01 Blood pressure: Reg exercise: low 35, moderate 62, high 25 No reg. Exercise: low 21, moderate 65, high 28 arrow_forward
- In a study conducted in the Science Department of Faculty of Science, Technology and Human Development in a University; the researcher examined the influence of the drug succinylcholine on the circulation levels of androgens in the blood. Blood samples from wild, free-ranging deer were obtained via the jugular vein immediately after an intramuscular injection of succinylcholine using darts and a capture gun. Deer were bled again approximately 30 minutes after the injection and then released. The level of androgens at time of capture and 30 minutes later, measured in nanograms per milliliter (ng/ml), for 15 deers as in Table Q1. Assuming that the populations of androgen at time of injection and 30 minutes later are normally distributed:i) Find the average and standard deviation of this studyii)Determine the critical region of this problem.iii) Test at the 0.05 level of significance whether the androgen concentrations are altered after 30 minutes of restraint.arrow_forwardA psychologist at a private mental hospital was asked to determine whether there was a clear difference in the length of stay for patients with different categories of diagnosis. Looking at the last four patients in each of the three major categories, the results (in terms of weeks of stay) were as follows: Diagnosis Category Affective Disorders Cognitive Disorders Drug-Related Conditions 7 12 8 6 8 10 5 9 12 6 11 10 Using alpha = 0.05, is there a significant difference in length of stay among diagnosis categories? Show all five steps of hypothesis testing. For additional practice, compute the means and standard deviations for each group. What is the purpose of a post hoc test? What does it tell us? Explain why we do not need a post hoc test if there are only two groups in our study. Conduct Tukey's HSD post hoc test to determine where there is a difference in the three groups.arrow_forwardA psychologist at a private mental hospital was asked to determine whether there was a clear difference in the length of stay for patients with different categories of diagnosis. Looking at the last four patients in each of the three major categories, the results (in terms of weeks of stay) were as follows: Diagnosis Category Affective Disorders Cognitive Disorders Drug-Related Conditions 7 12 8 6 8 10 5 9 12 6 11 10 Using alpha = 0.05, is there a significant difference in length of stay among diagnosis categories? Show all five steps of hypothesis testing and compute the means and standard deviations for each group.arrow_forward
- The article “Treadmill Exercise and Resistance Training in Patients With Peripheral Arterial Disease With and Without Intermittent Claudication. A Randomized Controlled Trial” (M. McDermott, P. Ades, et al., Journal of the American Medical Association, 2009:165–174) reported the results of a study to determine whether treadmill exercise could improve the walking ability of patients suffering from claudication, which is pain caused by insufficient blood flow to the muscles of the legs. A sample of 48 patients walked on a treadmill for six minutes every day. After six months, the mean distance walked in six minutes was 348 m, with a standard deviation of 80 m. For a control group of 46 patients who did not walk on a treadmill, the mean distance was 309 m with a standard deviation of 89 m. Find a 95% confidence interval for the difference in mean distance walked between the two groups of patients.arrow_forwardThe article “Treadmill Exercise and Resistance Training in Patients With Peripheral Arterial Disease With and Without Intermittent Claudication. A Randomized Controlled Trial” (M. McDermott, P. Ades, et al., Journal of the American Medical Association, 2009:165–174) reported the results of a study to determine whether treadmill exercise could improve the walking ability of patients suffering from claudication, which is pain caused by insufficient blood flow to the muscles of the legs. A sample of 48 patients walked on a treadmill for six minutes every day. After six months, the mean distance walked in six minutes was 348 meters, with a standard deviation of 80 m. For a control group of 46 patients who did not walk on a treadmill, the mean distance was 309 m with a standard deviation of 89 m. Can you conclude that the mean distance walked for patients using a treadmill is greater than the mean for the controls? Use the α = 0.05 level of significance.arrow_forwardA researcher was interested in studying if there is a significant relationship between the severity of COVID 19 and blood types of individuals. 2400 individuals were studied and the results are shown below. Condition Blood Type O A B AB Total Critical 64 44 20 8 136 Severe 175 129 50 15 369 Moderate 211 528 151 125 1015 Mild 200 400 140 140 880 Total 650 1101 361 288 2400 State both the null and alternative, Provide the decision rule for making this Use an alpha level of 5%, Show all of the work necessary to calculate the appropriate, What conclusion are you allowed to draw? Would your conclusion change at the 10% level of significance?arrow_forward
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