You may need to use the appropriate technology to answer this question. Three admission test preparation programs are being evaluated. Suppose the scores obtained by a sample of 20 people who used the programs provided the following data. Program A B C 530 450 600 400 530 640 480 400 570 540 410 480 480 470 580 610 390 620 550 590 Use the Kruskal-Wallis test to determine whether there is a significant difference among the three test preparation programs. Use 𝛼 = 0.05. State the null and alternative hypotheses. H0: All populations of test scores are identical. Ha: Not all populations of test scores are identical. H0: MedianA = MedianB = MedianC Ha: MedianA ≠ MedianB ≠ MedianC H0: MedianA ≠ MedianB ≠ MedianC Ha: MedianA = MedianB = MedianC H0: MedianA = MedianB = MedianC Ha: MedianA > MedianB < MedianC H0: Not all populations of test scores are identical. Ha: All populations of test scores are identical. Find the value of the test statistic. (Round your answer to two decimal places.) test statistic= Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Reject H0. There is not sufficient evidence to conclude that there is a significant difference among the three test preparation programs. Do not reject H0. There is not sufficient evidence to conclude that there is a significant difference among the three test preparation programs. Do not reject H0. There is sufficient evidence to conclude that there is a significant difference among the three test preparation programs. Reject H0. There is sufficient evidence to conclude that there is a significant difference among the three test preparation programs.
Added by Michaela B.
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First, we need to state the null and alternative hypotheses: $H_0: \text{Median}_A = \text{Median}_B = \text{Median}_C$ $H_a: \text{At least one median is different}$ Show more…
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A large corporation sends many of its first-level managers to an off-site supervisory skills training course. Four different management development centers offer this course. The director of human resources would like to know whether there is a difference among the quality of training provided at the four centers. An independent random sample of five employees was chosen from each training center. The employees were then ranked 1 to 20 in terms of supervisory skills. A rank of 1 was assigned to the employee with the best supervisory skills. Suppose the ranks are as shown. Course A B C D 5 2 16 19 14 9 18 3 8 4 10 13 15 1 17 6 11 12 20 7 Use α = 0.05 and test whether there is a significant difference among the quality of training provided by the four programs. State the null and alternative hypotheses. H0: There is no difference in the quality of the training for the programs. Ha: There is a difference in the quality of the training for the programs. H0: MedianA = MedianB = MedianC = MedianD Ha: MedianA ≠ MedianB ≠ MedianC ≠ MedianD H0: MedianA = MedianB = MedianC = MedianD Ha: MedianA ≠ MedianB ≠ MedianC ≠ MedianD H0: There is a difference in the quality of the training for the programs. Ha: There is no difference in the quality of the training for the programs. H0: MedianA = MedianB = MedianC = MedianD Ha: MedianA > MedianB < MedianC > MedianD Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Reject H0. There is sufficient evidence to conclude that there is a significant difference among the quality of training provided by the four programs. Do not reject H0. There is sufficient evidence to conclude that there is a significant difference among the quality of training provided by the four programs. Do not reject H0. There is not sufficient evidence to conclude that there is a significant difference among the quality of training provided by the four programs. Reject H0. There is not sufficient evidence to conclude that there is a significant difference among the quality of training provided by the four programs.
Adi S.
Consider the data. xi 1 2 3 4 5 yi 4 6 5 11 14 (a) Compute the mean square error using equation s2 = MSE = SSE n − 2 . (Round your answer to two decimal places.) (b) Compute the standard error of the estimate using equation s = MSE = SSE n − 2 . (Round your answer to three decimal places.) (c) Use the t test to test the following hypotheses (𝛼 = 0.05): H0: 𝛽1 = 0 Ha: 𝛽1 ≠ 0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Do not reject H0. We conclude that the relationship between x and y is significant. Reject H0. We conclude that the relationship between x and y is significant. Do not reject H0. We cannot conclude that the relationship between x and y is significant. Reject H0. We cannot conclude that the relationship between x and y is significant. (d) Use the F test to test the hypotheses in part (c) at a 0.05 level of significance. Present the results in the analysis of variance table format. Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to three decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Regression Error Total Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Do not reject H0. We cannot conclude that the relationship between x and y is significant. Reject H0. We conclude that the relationship between x and y is significant. Do not reject H0. We conclude that the relationship between x and y is significant.Reject H0. We cannot conclude that the relationship between x and y is significant.
An experiment has been conducted for four treatments with eight blocks. Complete the following analysis of variance table. (Round your values for mean squares and F to two decimal places, and your p-value to three decimal places.) Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value --------------------- | -------------- | ------------------ | ----------- | - | ------- Treatments | 300 | | | | Blocks | 400 | | | | Error | | | | | Total | 900 | | | | Use α = 0.05 to test for any significant differences. State the null and alternative hypotheses. H0: μ1 = μ2 = μ3 = μ4 Ha: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Reject H0. There is sufficient evidence to conclude that the means of the four treatments are not all equal.
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