22. What is the power of each of the following studies, using a t test for dependent means (based on the .05 significance level)? (a) (b) (C) (d) (e) (1) (g) Effect Size Small Medium Large Small Small Small Small N 50 50 50 10 40 100 100 Tails Two Two Two Two Two Two One
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- For the following problem, provide the following: Test statistic p-value Interpretation of the results in the context of the problem Cases of UFO sightings are randomly selected and categorized according to month, with the results listed in the table below (based on data from Larry Hatch). Use a .05 significance level to test the claim that UFO sightings occur in the different months with equal frequency. Is there any reasonable explanation for the two months that have the highest frequencies? Month: 1 2 3 4 5 6 7 8 9 10 11 12 1239 1111 1428 1276 1102 1225 2233 2012 1680 1994 1648 1125You wish to test the following claim (Ha) at a significance level of a - 0.005. Ho: P1= P2 Ha: P1 P2 You obtain 9.9 % successes in a sample of size ₁ 455 from the first population. You obtain 7.7% successes in a sample of size n₂ 797 from the second population. Round values for X to the nearest whole number. What is the test statistic for this sample? (Round to three decimal places.) test statistic = What is the p-value for this sample? (Round to four decimal places.) p-value EYou wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. Ho:μ1=μ2Ho:μ1=μ2 Ha:μ1<μ2Ha:μ1<μ2You obtain the following two samples of data. Sample #1 Sample #2 41.9 43.9 54.4 59.3 65.1 75.1 47.8 53.5 49.7 66.3 62.1 49.1 28.1 42.8 56.4 43.6 35.6 38.1 38.1 58.2 40.2 42.8 57.1 53.5 64 48.4 28.1 28.1 51.3 54.4 44.7 61.3 41.1 51.3 51.3 66.3 75.1 47.5 60.4 48.4 34.8 37.5 54.4 39.2 43.2 55.1 33.2 34 61.7 57.4 36.3 50.3 37.5 40.6 41.1 60.8 56.8 61.3 42.3 40.7 45.1 53.6 40 56.2 42.8 50.4 57.4 53.4 60.7 61 68.1 55.6 55.1 53.6 49.9 53.2 65.7 49.5 52.8 45.4 54.5 58.9 58.9 50.8 60.1 54.3 66.4 56.2 51.3 53.4 52.3 52.3 64.6 53.4 53.6 55.8 64.1 46.6 57.9 48 59.8 58.9 64.6 54.1 47.7 63.6 59.5 54.7 50.6 What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? For this calculation, use the…
- 5.32 Fuel efficiency of manual and automatic cars, Part I: Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? Assume that conditions for inference are satisfied. City MPG, Automatic City MPG, Manual Mean 16.12 19.85 SD 3.58 4.51 n 26 26 The test statistic is:The p-value is:You wish to test the following claim (Hå) at a significance level of a Ho: P₁ = P2 Ha: P₁ P2 0.005. You obtain 10.2% successes in a sample of size ni 518 from the first population. You obtain 15.2% successes in a sample of size n₂ 269 from the second population. Round values for X to the nearest whole number. What is the test statistic for this sample? (Round to three decimal places.) test statistic = What is the p-value for this sample? (Round to four decimal places.) p-value =You wish to test the following claim (H) at a significance level of a = 0.001. Ho: P₁ ≤ P2 Ha: P₁ P2 You obtain 194 successes in a sample of size n₁ in a sample of size n₂ = 365 from the second population. - test statistic = p-value = 240 from the first population. You obtain 273 successes [three decimal accuracy] [three decimal accuracy]
- You wish to test the following claim (Ha) at a significance level of =0.01. Ho:μ1=μ2 Ha:μ1≠μ2You obtain the following two samples of data. Sample #1 Sample #2 102.7 70.5 101.6 113.4 79 96 76.5 89.9 79.8 101.6 109.9 71.6 77.6 83.5 75.4 87 106.7 82.1 94.7 88.1 91.1 91.6 91.4 99 96.4 70.5 92.5 111.4 103.2 93.4 80.2 107.6 113.4 101.6 71.6 106.7 88.4 82.5 84.8 94.4 76.5 70.5 100.2 91.9 100.7 67.8 89.6 97.8 89 90.5 67.8 106.7 74 78.1 93.1 91.9 85.8 105.2 81.4 91.4 80.6 87.9 106.9 109.4 102.4 60.4 104.9 89.5 72.4 84.9 84.5 97.4 77.1 72.9 92.7 100.3 94 81.1 79.2 104 84.2 83 86 89.5 64.9 93.6 84.9 87.1 105.8 90.2 66.6 94.9 89.5 74.9 92.3 88.3 83.8 64 68.1 91.9 80.7 83.8 85.6 99.1 93.1 89.1 90.2 94 64.9 71.8 105.8 96.9 84.2 75.3 86 56.9 112.9 84.5 96.9 What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this…You wish to test the following claim (H) at a significance level of a = 0.001. Ho: 112 Ha:> H2 You obtain the following two samples of data. Sample #1 65.2 79.3 87.1 48.3 85.7 51.7 42.6 58.3 56.5 94.7 61.1 86.4 91.8 71 68.1 58.3 68.1 109.3 103.6 35 67.2 52.5 98.4 114.5 79.3 83.2 57.2 63.2 101.6 56.5 94.7 76.8 55.9 31.7 67.2 55.9 81 26.5 43.9 Sample #2 84.2 49.5 59.9 70.9 40.5 79.7 50.1 58.9 71.9 16.9 53.8 69.3 55.6 65.6 65.6 75.4 42.5 45.8 74.8 44.2 30.9 67.7 59.9 72.5 66.1 47.3 90.9 53.3 85.8 66.7 39.5 68.7 80.4 30.9 57.3 61.5 79.1 68,2 57.8 39.5 64.6 34.3 58.3 56.7 59.4 83.4 69.3 57.3 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.) p-value =You wish to test the following claim (H) at a significance level of a = 0.001. H₂: P₁ = P2 Ha: P₁ P2 You obtain 61.9% successes in a sample of size ₁ = 423 from the first population. You obtain 53.1% successes in a sample of size n₂ = 531 from the second population. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value= The p-value is... less than (or equal to) a greater than a This test statistic leads to a decision to... O reject the null accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion. There is not sufficient evidence to warrant rejection of the claim that the first population proportion is not equal to the second population proprtion. The sample data…
- You wish to test the following daim (Ha) at a significance level of a = 0.005. H.:P1 > P2 Ha:P1 < P2 You obtain a sample from the first population with 303 successes and 238 failures. You obtain a sample from the second population with 155 successes and 79 failures. critical value = [three decimal accuracy] test statistic = [three decimal accuracy] The test statistic is... O in the critical region O not in the critical region This test statistic leads to a decision to... reject the null hypothesis fail to reject the null hypothesis As such, the final condusion is that... O There is sufficient evidence to support that the first population proportion is less than the second population proportion. O There is not sufficient evidence to support that the first population proportion is less than the second population proportion.Measurements of the sodium content in samples of two brands of chocolate yielded the following results: Brand A- n= 9, s = 2.642 , Brand B- n 13, s = 6.409 . Can you conclude, at the 1% significance level, that the sodium content is more variable in Brand B ? (Assume that sodium content is normally distributed.) (A) Yes (B) NoYou wish to test the following claim (Ha) at a significance level of a = 0.001. Ho: P1 = P2 Ha: P₁ P2 You obtain 690 successes in a sample of size ₁ = 755 from the first population. You obtain 529 successes in a sample of size n2 = 603 from the second population. What is the critical value for this test? (Round to three decimal places.) Critical value = What is the test statistic for this sample? (Round to three decimal places.) Test statistic = The test statistic is... in the critical region not in the critical region This test statistic leads to a decision to... O reject the null O fail to reject the null As such, the final conclusion is that... O The sample data support the claim that the first population proportion is greater than the second population proportion. O There is not sufficient sample evidence to support the claim that the first population proportion is greater than the second population proportion.
