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A study was performed to test the effectiveness of aspirin in the treatment of
strokes. There were 155 patients in the study. A random sample of 78 of these
patients were placed in the “aspirin” group, and the remaining 77 in the “control”
group. After six months of treatment, all the patients were evaluated and their
condition recorded as either favorable or unfavorable. Of the 78 “aspirin” patients,
63 had favorable outcomes; of the 77 “control” patients, 43 had favorable
outcomes. We want to test the null hypothesis that the percentage of favorable
outcomes is the same between the two conditions.
Calculate the p-value and express what it means in plain words.
Do you reject the null hypothesis? State your conclusion in the context of the
original problem.
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- What is an experiment?A study was performed to test the effectiveness of aspirin in the treatment of strokes. There were 200 patients in the study. A random sample of 110 of these patients were placed in the “aspirin” group, and the remaining 90 in the “control” group. After six months of treatment, all the patients were evaluated and their condition recorded as either favorable or unfavorable. Of the 110 “aspirin” patients, 72 had favorable outcomes; of the 90 “control” patients, 53 had favorable outcomes. We want to test the null hypothesis that the percentage of favorable outcomes is the same between the two conditions. Write down the box model for the null hypothesis as a sentence or picture of the box. Under the null hypothesis, the difference in the sample percentages is expected to be ________%, and the standard error for the difference is ________%. Calculate the appropriate two-sample z test statistic. Calculate the p-value and express what it means in plain…A study was undertaken to investigate the effectiveness of an aquarobic exercise program for patients with osteoarthritis. A convenience sample of 70 individuals with arthritis was selected, and each person was randomly assigned to one of two groups. The first group participated in a weekly aquarobic exercise program for 8 weeks; the second group served as a control. Several pieces of data were collected from the individuals, including their total cholesterol (mg). Determine if there is a significant difference in the mean cholesterol for the two groups (aquarobic & control) at the start of the study using a significance level of 0.01. Difference Sample Diff. Std. Error df Aquarobic - Control -13.9045 6.8214 67.8635 What hypotheses should be tested? Make sure to select the hypotheses which are written with notation consistent with the type of samples selected. Ho:μd=0Ho:μd=0Ha:μd>0Ha:μd>0 Ho:μd=0Ho:μd=0Ha:μd<0Ha:μd<0 Ho:μ1=μ2Ho:μ1=μ2Ha:μ1<μ2Ha:μ1<μ2…
- A study was performed to test the effectiveness of aspirin in the treatment of strokes. There were 155 patients in the study. A random sample of 78 of these patients were placed in the “aspirin” group, and the remaining 77 in the “control” group. After six months of treatment, all the patients were evaluated and their condition recorded as either favorable or unfavorable. Of the 78 “aspirin” patients, 63 had favorable outcomes; of the 77 “control” patients, 43 had favorable outcomes. We want to test the null hypothesis that the percentage of favorable outcomes is the same between the two conditions. (a) Write down the box model for the null hypothesis as a sentence or picture of the box. (b) Under the null hypothesis, the difference in the sample percentages is expected to be ________%, and the standard error for the difference is ________%. (c) Calculate the appropriate two-sample z test statistic. (d) Calculate the p-value and express what it means in plain words. (e) Do…An experiment was conducted for better understanding of the effectiveness of a particular type of drug for reducing bad cholesterol (LDL) level. The purpose of the experiment was to determine whether different dosages used have significant different outcomes in average LDL reduction. Twenty subjects with LDL at around 250 to 300 mg/dL had participated in the study and were randomly divided into four groups. Each group was given a specific level of dosage of the drug each day for one month, with a control group that only provided with placebo. The reduction in LDL was recorded and showed in the following table. Positive number indicates reduction and negative numbers indicates increasing in DLD. Use statistical software to analyze the data and answer the following question. Control Light Dosage Level Medium Dosage Level Heavy Dosage Level 7 25 73 81 -3 17 60 71 6 22 55 79 5 21 41 60 15 12 36 85 Perform a One-way…A study was undertaken to investigate the effectiveness of an aquarobic exercise program for patients with osteoarthritis. A convenience sample of 70 individuals with arthritis was selected, and each person was randomly assigned to one of two groups. The first group participated in a weekly aquarobic exercise program for 8 weeks; the second group served as a control. Several pieces of data were collected from the individuals, including their total cholesterol (mg). Determine if there is a significant difference in the mean cholesterol for the two groups (aquarobic & control) at the start of the study using a significance level of 0.01. Difference Sample Diff. Std. Error df Aquarobic - Control 4.8006 8.4711 59.5847 What hypotheses should be tested? Make sure to select the hypotheses which are written with notation consistent with the type of samples selected. Ho:μ1=μ2Ho:μ1=μ2Ha:μ1>μ2Ha:μ1>μ2 Ho:μd=0Ho:μd=0Ha:μd>0Ha:μd>0 Ho:μd=0Ho:μd=0Ha:μd≠0Ha:μd≠0…
- A study was undertaken to investigate the effectiveness of an aquarobic exercise program for patients with osteoarthritis. A convenience sample of 70 individuals with arthritis was selected, and each person was randomly assigned to one of two groups. The first group participated in a weekly aquarobic exercise program for 8 weeks; the second group served as a control. Several pieces of data were collected from the individuals, including their total cholesterol (mg). Determine if there is a significant difference in the mean cholesterol for the two groups (aquarobic & control) at the start of the study using a significance level of 0.10. Difference Sample Diff. Std. Error df Aquarobic - Control 2.698 7.3227 65.6844 • What hypotheses should be tested? Make sure to select the hypotheses which are written with notation consistent with the type of samples selected. H.: µd = l2 H.: µ1 = µ2 H.:µd H.: Hd > 0 Ha: H1 # H2 Ha:µ1 > µ2 Ha:Hd < 0 Ha:H1 < µs Ha: Hd # 0 = 0 H,:µ1 0 H.: µ1 = µ2 H.: µd •…The inflammation caused by osteoarthritis of the knee can be very painful and can inhibit movement. Leech saliva contains anti-inflammatory substances. To study the therapeutic effect of attaching four to six leeches to the knee for about 70 minutes, 51 volunteers were randomly assigned to receive either the leech treatment or a topical gel, diclofenac. This summary table gives the results of a pretreatment measure of the amount of pain reported by the two groups, before beginning therapy. A higher score means more pain. The researchers hoped that the randomization would result in two comparable groups with respect to this variable. You may assume that the pain scores are approximately normal for each group. Leech (Group 1): x⎯⎯⎯x¯ = 52.4, ss = 13.9, nn = 24Topical gel (Group 2): x⎯⎯⎯x¯ = 52, ss = 16.6, nn = 27 Unless otherwise stated, give your answers to three decimal places. Construct a 99% confidence interval for the difference in average pain score. Give your answers to two…Kava is a beverage or extract that is made from Piper methysticum, a plant native to the western Pacific islands. Suppose that, in a randomized comparative experiment to determine if taking kava daily can reduce insomnia, a group of participants with insomnia were randomly assigned to take kava (treatment group) or a placebo (control group). After six weeks, the participants were interviewed to see if they experienced a decrease in insomnia. The table shows the results from the sample. The counts are the number of people in each group who experienced a decrease in insomnia. Group Description Population proportion Sample size Sample count Sample proportion 1 Treatment (kava) P1 n₁ = 402 x1 = 213 P₁ = 0.5299 2 Control (placebo) P2 n₂ = 521 x₂ = 121 P2 = 0.2322 Compute the standard error estimate, SE, of the difference in the sample proportions. Give your answer to at least four decimal places. 0.0438 SE = Incorrect Determine the value of the two-sample z-statistic for the difference in…
- 3. A researcher was interested in the effects of a drug on depression. Subjects were randomly assigned to one of the three groups. Subjects in the control group received a placebo and the subjects in the two treatment groups received either a 0.2 mg or a 0.4 mg dosage of the drug. After several weeks of drug (or placebo) treatment, the researcher measured the subjects' level of depression (a low score indicating greater depression) The following data were obtained. Placebo 0.2 mg 0.4 mg 12 11 12 8 10 9 9 14 11 11 17 13 13 16 15 7 16 12 Mean of X = 10 14 12 S^2 = 5.6 8.4 4 Using 5% of significance, test the hypothesis that the three groups differ in their effectiveness.In Hong Kong, some employers claim that they are willing to offer betterstarting salaries for those university graduates with a higher GPA. A study on Hong Kong university students was carried out. A simple random sample of 96 students who were admitted to Hong Kong universities between 2010 and 2013 was selected. Final cumulative GPA and starting salary (monthly salary in Hong Kong Dollars) of each participant were collected. A scatterplot of the two variables (gpa = final cumulative GPA; salary = starting salary) is shown below.A behavioral scientist investigated whether there is a significant difference in the percentages of men and women who purchase silver-colored cars. The scientist selected a random sample of 50 men and a random sample of 52 women who had recently purchased a new car. Of the men selected, 16 had purchased a silver-colored car. Of the women selected, 9 had purchased a silver-colored car. Which of the following is the most appropriate method for analyzing the results? A two-sample zz-test for the difference in population proportions A A two-sample zz-test for the difference in sample proportions B A one-sample zz-test for a sample proportion C A one-sample zz-test for a population proportion D A one-sample zz-test for a difference in sample proportions