Consider the following hypothesis test. H: H> 0 (a) The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 - Population 2.) Population Element 1 2 Difference 21 18 2 28 27 3 18 17 4 20 18 5 26 23 (b) Compute d. (c) Compute the standard deviation s. (d) Conduct a hypothesis test using a = 0.05. Calculate the test statistic. (Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? O Do not reject Ho. There is insufficient evidence to conclude that u, > 0. O Reject H. There is sufficient evidence to conclude that u, >0. O Do not Reject Ho. There is sufficient evidence to conclude that u, > 0. O Reject H,. There is insufficient evidence to conclude that u,> 0.
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- Test whether µ, <µ, at the a = 0.01 level of significance for the sample data shown in the accompanying table. Assume that the populations are normally distributed. Click the icon to view the data table. Determine the null and alternative hypothesis for this test. A. Ho:H1A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random H samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: #₁ = 1₂ H₁: H₁ H₂ OC. Ho: H₁A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.10 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: Hq ZH₂ OC. Ho: H₁ H₂ H₁: Hy > H₂ The test statistic, t, is. (Round to two decimal places as needed.) (Round to three decimal places as needed.) The P-value is State the conclusion for the test. C... OB. Ho: H₁ H₂ H₁: Hy #H₂ OD. Ho: Hg #U2 H₁: HyGiven two dependent random samples with the following results: Population 1 35 34 45 30 49 25 34 Population 2 44 24 40 42 38 31 43 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that both populations are normally distributed. Step 2 of 4 : Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places. please highlight the answerA study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: H₁ H₂ OC. Ho: H₁ H¹/₂ H₁: H₁You may need to use the appropriate technology to answer this question. Consider the following hypothesis test. H0: ?d ≤ 0 Ha: ?d > 0 (a) The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 − Population 2.) Element Population Difference 1 2 1 21 19 2 28 28 3 18 17 4 20 18 5 26 26 (b) Compute d. (c) Compute the standard deviation sd. (d) Conduct a hypothesis test using ? = 0.05. Calculate the test statistic. (Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? Reject H0. There is insufficient evidence to conclude that ?d > 0. Reject H0. There is sufficient evidence to conclude that ?d > 0. Do not Reject H0. There is sufficient evidence to conclude that ?d > 0. Do not reject H0. There is insufficient evidence to conclude that ?d >…With the information provided, determine which hypothesis test is required, and per- form it as asked. A frequency table for two categorical variables X and Y, each with two levels, a = 0.05 significance level? given below. Is there evidence of a relationship between them at the X1 X2 Y1 101 81 Y2 35 52 (a) What are Ho and HA? (b) What is the relevant test statistic and its sampling distribution under the null hypothesis? (c) Calculate the test statistic and provide the value. Show working. (d) Using your preferred method (RoR, p-value, CI) make a determination about the hypothesis test.Q2. Use the sample data below to test the hypotheses H: P = P2 = P3 H: Not all population proportions are equal where pi is the population proportion of Yes responses for population i. Use a 0.1 level of significance to answer the following questions. Populations Response 1 2 Yes 150 140 100 No 100 140 100 (A). What is the test statistic value? (B). Observing the x table, what is the possible range of values of the p-value? [Multiple choice with single answer] (a) 0.01Test the claim below about the mean of the differences for a population of paired data at the level of significance a. Assume the samples are random and dependent, and the populations are normally distributed. Claim: H, 20; a = 0.05. Sample statistics: d = -2.2, s, = 1.5, n=14 Identify the null hypothesis by writing its complement. O A. Ho: Ha #0 Ha: H = 0 O B. Ho: Hg s0 Hgi Hg>0 O D. Ho: Ha 0 E. Ho: Ha 20 H: H <0 The test statistic is t= -5.49. (Round to two decimal places as needed.) The critical value(s) is(are) t, = - 1.77 (Round to two decimal places as needed. Use a comma to separate answers as needed.) V the rejection region, V the null hypothesis. There V statistically significant evidence to reject the claim. Since the test statistic isGiven two dependent random samples with the following results: Population 1 43 32 39 39 44 47 37 Population 2 34 19 36 29 46 35 41 Use this data to find the 90% confidence interval for the true difference between the population means. Let d = (Population 1 entry)-(Population 2 entry). Assume that both populations are normally distributed. Copy Data Step 3 of 4: Find the standard deviation of the paired differences to be used in constructing the confidence interval. Round your answer to one decimal place.Consider the following hypothesis test. Ho: H1 - H2 = 0 Ha: H1 - 42 # 0 The following results are from independent samples taken from two populations assuming the variances are unequal. Sample 1 Sample 2 n1 35 = 40 = 13.6 X, = 10.1 S1 5.8 S2 = 8.1 (a) What is the value of the test statistic? (Use x, - x2. Round your answer to three decimal places.) (b) What is the degrees of freedom for the t distribution? (Round your answer down to the nearest integer.) (c) What is the p-value? (Round your answer to four decimal places.) p-value = (d) At a = 0.05, what is your conclusion? Do not Reject Ho: There is sufficient evidence to conclude that u, - µ, ± 0. Reject Ho. There is sufficient evidence to conclude that µ, - µ, # 0. Do not Reject Ho. There is insufficient evidence to conclude that u, - H, + 0. 0' Reject Ho. There is insufficient evidence to conclude that u1 - µ2 ± 0.Test the claim below about the mean of the differences for a population of paired data at the level of significance a. Assume the samples are random and dependent, and the populations are normally distributed. Claim: H, 20; a= 0.05. Sample statistics: d= -2.2, s, =1.5, n= 14 Identify the null hypothesis by writing its complement. COA. Ho: Ha #0 H: Ho =0 OB. Ho: Pa s0 OC. Ho: Ha =0 OD. Ho: Ha 0 H: Hg <0 The test statistic is t= - 5.49. (Round to two decimal places as needed.) The critical value(s) is(are) t, = - 1.77. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Since the test statistic is V the rejection region, V the null hypothesis. There V statistically significant evidence to reject the claim.SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. 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