Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in golf tournaments are shown in the following table. First Final First Final Player Round Round Player Round Round Golfer 1 70 72 Golfer 11 72 72 Golfer 2 71 72 Golfer 12 72 70 Golfer 3 70 74 Golfer 13 70 73 Golfer 4 72 71 Golfer 14 70 76 Golfer 5 70 69 Golfer 15 68 70 Golfer 6 67 67 Golfer 16 68 65 Golfer 7 71 68 Golfer 17 71 70 Golfer 8 68 72 Golfer 18 70 68 Golfer 9 67 71 Golfer 19 69 68 Golfer 10 70 69 Golfer 20 67 71 Suppose you would like to determine if the mean score for the first round of a golf tournament event is significantly different than the mean score for the fourth and final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration cause scores to come down? (a) Use a = 0.10 to test for a statistically significantly difference between the population means for first- and fourth-round scores. State the null and alternative hypotheses. (Use . = mean score first round - mean score fourth round.) OHOH SO OH: H = 0 HA: H- =0 OH: H = 0 OH: H>0 OHo: My = 0 HA:H = 0 Calculate the value of the test statistic. (Round your answer to three decimal places.)Calculate the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Do not reject Ho. There is insufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round. O Reject Ho. There is insufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round. O Reject Ho. There is sufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round. O Do not Reject Ho. There is sufficient evidence to conclude that the mean score for the first round of a golf tournament is significantly different than the mean score for the fourth and final round. b) What is the point estimate of the difference between the two population means? (Use mean score first round - mean score fourth round.) For which round is the population mean score lower? The mean of the fourth round scores was lower than the mean of the first round scores. O The mean of the first round scores was lower than the mean of the fourth round scores.Consider the following hypothesis test, Hoiu, =10 o7 d ~ {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 4 (b} Compute d. L ] (c) Compute the standard deviation 5. (d} Conduct a hypothesis test using o = 0.05. Calculate the test statistic. (Round your answer to three decimal places.} L ] Calculate the p-value. (Round your answer to four decimal places.) What is your conclusion? () Do not Reject Hy. There is sufficient evidence to conclude that i , > 0. () Do not reject H . There is insufficient evidence to conclude that p > 0. () Reject HD' There is insufficient evidence to conclude that By 0. () Reject Hy. There is sufficient evidence to conclude that i, = 0. A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow. Student Math Writing 540 474 2 432 380 3 528 463 4 574 612 5 448 420 502 526 7 480 430 8 499 459 610 615 10 572 541 11 390 335 12 593 613 (a) Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score - writing score.) Formulate the hypotheses. O H : H=0 O Ho:H20 O O Ho:H-=0 O 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 Hy. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test. ) Do not reject Hy. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test. ) Reject Hy. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test. ) Do not reject Hy. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test. (b} What is the point estimate of the difference between the mean scores for the two tests? (Use math score writing score. ) What are the estimates of the population mean scores for the two tests? Which test reports the higher mean score? The math test reports a mean score than the writing test. Consider the following hypothesis test. H: 0 1 2 =07 $ 2 + 07 (a) What is your conclusion if n, = 21, s, 2 = 8.2, n2 = 26, and s2 2 = 4.0? Use a = 0.05 and the p-value approach. Find the value of the test statistic. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Reject Ho. We cannot conclude that o, 2 = 0, 2. O Do not reject Ho. We cannot conclude that o, State your conclusion. O Reject Ho. We cannot conclude that o,