a) Select the appropriate null and alternative hypotheses for investigating whether the new method is any different to the old one. ? denotes the population proportion that improve under the new method, and p denotes the proportion that improved under the new method within the sample above. H0 : ? ? 0.31; HA : ? = 0.31 H0 : ? = 0.31; HA : ? ? 0.31 H0 : ? = 0.31; HA : ? ? 0.33 H0 : p = 0.31; HA : p ? 0.31 H0 : ? = 0.33; HA : ? ? 0.33 b) What proportion of patients had their eyesight recovered in the new method in the sample. c) Find the standardized test statistic for this study. d) Calculate the p-value for this test. e) Given the p-value calculated in part d) and ? = 0.05, select the conclusion which would be appropriate for this hypothesis test. The p-value is greater than or equal to 0.05. There is evidence to reject H0. There is evidence to suggest the percentage who recover their eyesight with the new method is different to the percentage who recover their eyesight under the old method. The p-value is less than 0.05. There is evidence to reject H0. There is evidence that the percentage who recover their eyesight with the new method is different from the percentage who recover their eyesight with the old method. The p-value is less than 0.05. There is insufficient evidence to reject H0. There is not sufficient evidence to conclude that the percentage who recover their eyesight with the new method is significantly different to the percentage who recover their eyesight under the old method. The p-value is greater than or equal to 0.05. There is insufficient evidence to reject H0. There is not sufficient evidence to conclude that the percentage who recover their eyesight with the new method is different to the percentage who recover their eyesight under the old method.
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a) We want to test if the new method is different from the old one, so the null hypothesis should state that the proportions are the same, and the alternative hypothesis should state that the proportions are different. Show more…
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A team of eye surgeons have developed a new technique to restore the sight of people blinded from a certain disease. Under the old method it is known that only 31% of patients who undergo this operation recover their eyesight. In a random sample of 299 operations performed using the new method, 100 patients fully recovered their eyesight. a) Select the appropriate null and alternative hypotheses for investigating whether the new method is any different to the old one. π denotes the population proportion that improve under the new method, and p denotes the proportion that improved under the new method within the sample above. 1) H0 : π ≠ 0.31 ; HA : π = 0.31 2) H0 : π = 0.31 ; HA : π ≠ 0.31 3) H0 : μ = 0.31 ; HA : μ ≠ 0.33 4) H0 : p = 0.31 ; HA : p ≠ 0.31 5) H0 : π = 0.33 ; HA : π ≠ 0.33 b) What proportion of patients had their eyesight recovered in the new method in the sample. c) Find the standardized test statistic for this study. d) Calculate the p-value for this test. e) Given the p-value calculated in part d) and α=0.05, select the conclusion which would be appropriate for this hypothesis test. 1) The p-value is greater than or equal to 0.05. There is evidence to reject H0. There is evidence to suggest the percentage who recover their eyesight with the new method is different to the percentage who recover their eyesight under the old method. 2) The p-value is less than 0.05. There is evidence to reject H0. There is evidence that the percentage who recover their eyesight with the new method is different from the percentage who recover their eyesight with the old method. 3) The p-value is less than 0.05. There is insufficient evidence to reject H0. There is not sufficient evidence to conclude that the percentage who recover their eyesight with the new method is significantly different to the percentage who recover their eyesight under the old method. 4) The p-value is greater than or equal to 0.05. There is insufficient evidence to reject H0. There is not sufficient evidence to conclude that the percentage who recover their eyesight with the new method is different to the percentage who recover their eyesight under the old method.
Qudsiya A.
Case 5. Use the info given below to answer the five questions that follow. A corporation randomly selects 200 salespeople and finds that 156 who have never taken a self-improvement course would like to take such a course. The firm did a similar study 10 years ago in which 112 of a random sample of 170 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let p1 and p2 represent the true proportion of workers who would like to attend a self-improvement course in the current study and the past study respectively. The firm wants to test whether their current course recruitment efforts resulted in a greater proportion of workers that want to attend a self-improvement course than in the past. 23. What are the correct null and alternative hypotheses for the above situation? A. H0: p1 ≤ p2 Ha: p1 > p2 B. H0: μ1 ≥ μ2 Ha: μ1 < μ2 C. H0: p1 = p2 Ha: p1 ≠ p2 D. H0: p1 ≥ p2 Ha: p1 < p2 E. H0: μ1 = μ2 Ha: μ1 ≠ μ2 24. What is the pooled or common proportion that attend the self-improvement course? A. 0.78 B. 0.66 C. 0.72 D. 0.12 E. 1.39 25. What is the sample difference between the proportions (i.e., as found in the samples)? B. 0.78 B. 0.66 C. 1.39 D. 0.72 E. 0.12 26. What is the critical (table) value for the test of hypothesis for this problem if α = 0.01? C. 1.645 B. 2.33 C. 1.96 D. 2.57 E. 1.28 27. If the computed test statistic is 1.06, what are the decision and conclusion of the test at the 0.01 significance level? A. Fail to reject the null hypothesis, conclude there is sufficient evidence that the proportion of workers that want to attend the course has decreased. B. Reject the null hypothesis; conclude there is no evidence of difference in proportions. C. Fail to reject the null hypothesis, conclude there is sufficient evidence of difference in proportions. D. Reject the null hypothesis, conclude there is evidence that the proportion of workers that want to attend the course has increased. E. Fail to reject the null hypothesis, conclude there is insufficient evidence that the proportion of workers that want to attend the course has increased.
Danielle F.
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