You may need to use the appropriate technology to answer this question. In a completely randomized design, 13 experimental units were used for the first treatment, 14 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.) Source Sum Degrees Mean F of Variation of Squares of Freedom Square p-value Treatments 1,400 2 700 51.3332 Error 600 44 13.6364 Total 2,000 46 At a 0.05 level of significance, is there a significant difference between the treatments? State the null and alternative hypotheses. O Ho: At least two of the population means are equal. Ha: At least two of the population means are different. O Ho: H1 = H2 = H3 Ha: M1 = 12 * 13 OHo: H1 = H2 = H3 Ha: Not all the population means are equal. OHo: H1 = 12 * H3 Ha: H1 = H2 = H3 O Ho: Not all the population means are equal. Ha: M1 = M2 = H3 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value =You may need to use the appropriate technology to answer this question. In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equalisize towels were used, with four sections of towels tested per brand. The absorbency rating data follow. Brand x y z 90 98 B4 100 96 El? 87 93 90 91 97 79 At a 0.05 level of signicance, does there appear to be a difference in the ability of the brands to absorb water? State the null and alternative hypotheses. H03llle'1yzl'z Ha: Not all the population means are equal. O HO: Not all the population means are equal. Ha: \"x = ill'y = \"z O HO: uxyyipz Ha: \"x : J\"y : \"z Ooix=y=z Ha: pix i .nyr 1 #2 O HO: At least two of the population means are equal. Ha: At least two of the population means are different. a! Find the value of the test statistic. (Round your answer to two decimal places.) :I Find the pivalue. (Round your answer to three decimal places.) grate vnur conch nn. Find the sample means ofjob satisfaction for the remaining professions. inff JPN... XSA II S The overall sample mean I is the mean of all 40 observations and will be used in the calculations for the variance. 43+41+...+55+??+...+55+55+n.+?T+|Sl 40 The sample variance of job satisfaction for lawvers is calculated as follows, the final result rounded to three decimal places. = 2 5L2 ElixiX} n 1 {43 so]2 + {41 so}2 + ... + [as 5012 9 MEI II = 126.222 Find the remaining sample variances of job satisfaction for each profession, rounding the results to three decimal places. 2 SP1. = amass x 2 _ 5c E 2 Egg. E Step 3 The sample means and variances of the observed data are needed to find the values in the sum of squares column. The given data are below. Lawyer Physical Therapist Cabinetmaker Systems Analyst 43 56 55 45 41 77 66 72 75 79 78 72 43 87 70 59 52 59 78 63 51 58 63 65 44 63 58 42 49 53 77 54 63 56 85 77 39 51 61 61 The sample mean job satisfaction for lawyers is calculated as follows. X = . 43 + 41 + . . . + 39 10 = 50.0 Find the sample means of job satisfaction for the remaining professions. XPT = 63.9 *C = 69.1 *SA = 61.0 The overall sample mean x is the mean of all 40 observations and will be used in the calculations for the variance. X = = 43 + 41 + . . . + 56 + 77 + . . . + 55 + 66 + .. . + 77 +61 40 = 61 The sample variance of job satisfaction for lawyers is calculated as follows, the final result rounded to three decimal places