Use Critical Values for the Student's t Distribution Table to find the critical value or values for the following 00 significance level a, sample size n, and alternate hypothesis H₁. Part 1 of 2 (a) a = 0.05, n= t = 1.714 Part: 1 / 2 Part 2 of 2 24, and H₁: > Ho (b) a= 0.05, n=25, and H₁: u‡μ₁ t = X S E > olo
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- A) find the critical value(s) assuming that the population variances are equal . B) Find the critical value (s) assuming that they population variances are not equal.You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. Ho:μ1=μ2Ho:μ1=μ2 Ha:μ1≠μ2Ha:μ1≠μ2You believe both populations are normally distributed, but you do not know the standard deviations for either. We will assume that the population variances are not equal. You obtain a sample of size n1=17 with a mean of M1=64.6 and a standard deviation of SD1=11.7 from the first population. You obtain a sample of size n2=17 with a mean of M2=53.2 and a standard deviation of SD2=8.9 from the second population.What is the test statistic for this sample? (Report answer accurate to three decimal places.)You wish to test the following claim (H0,Ha) at a significance level of α=0.002 Ho:μ1=μ2 Ha:μ1≠μ2You obtain the following two samples of data. Sample #1 Sample #2 91.1 91.9 75.1 68.6 77.8 97 81.3 76.3 95 89.6 75.1 81.3 93.6 85.7 82.7 78.9 99.4 87.8 91.9 95.5 71.9 73.8 92.7 86.7 79.3 71.4 60.2 95 75.9 72.4 71.4 73.8 86.7 82.7 75.9 78.2 64.9 92.7 85 99.4 89.6 97 80 83.7 68.6 100.1 96.5 98.8 79.6 76.7 56.2 63.9 67.4 51.6 95.4 78.6 63.1 71.3 93.3 105.2 70.3 68 64.7 91.8 90.4 82.3 62.3 104.2 92.3 89.9 103.2 81.1 73.3 105.2 79.4 79.8 94.3 44.4 67.4 44.4 44.4 89 66.1 79 96.6 58.2 59.4 77.3 78.6 113 93.3 94.9 76.9 87.7 89.5 99.2 86 70.3 76 69.2 83.5 57 110.8 63.9 61.4 110.8 86.9 90.4 44.4 71.3 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…
- a. Find the t values that form the boundaries of the critical region for a two-tailed test with ? = .05 for a sample size of n = 12. b. Repeat the above for a one-tailed test, with ? = .05.You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01. Ho:μ1=μ2Ho:μ1=μ2 Ha:μ1≠μ2Ha:μ1≠μ2You obtain the following two samples of data. Sample #1 Sample #2 65.8 77.7 105.1 78.6 89.2 69.1 96.7 91.3 105.9 87.5 70.5 93.9 83.4 88.3 79.5 66.7 83.4 91.7 106.7 73 75.7 98.7 76.7 80 53.2 92.1 93 78.2 72.4 79.1 82.1 74.1 78.2 85.5 85.9 99.3 84.2 104.3 88.3 107.6 63.8 99.8 97.7 86.3 74.9 72.7 77.5 93.9 76.1 77.1 81.9 74.1 73.6 78.7 81.9 78.9 81.1 88 85.8 75.3 74.3 77.5 69.1 75.5 72.9 80.1 84.3 73.1 67.3 72.2 76.1 67.8 74.9 67.3 74.7 70.1 65.4 76.9 83.8 79.7 72.9 81.7 74.1 68.2 65.4 80.9 69.4 79.5 96 77.5 77.1 75.9 68.7 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…You wish to test the following claim (HaHa) at a significance level of α=0.05 Ho:μ1=μ2 Ha:μ1>μ2You obtain the following two samples of data. Sample #1 Sample #2 51.6 63.2 60 52.9 54.9 55.6 57.9 61.4 48.8 54.4 49.8 60.6 46 65.7 54.4 62.9 62 52 64.3 50.6 72.3 53.6 65 59.3 55.4 66.6 57.9 54 52.7 46.6 57.1 59.3 56.9 50.9 52.7 50.1 58.9 52 50.6 48.4 53.1 54.4 54.9 58.9 60.9 58.4 66.2 55.7 63.7 57.1 57.9 54 57.9 67.2 52.2 56.7 66.2 50.1 61.1 56.7 25.1 55.1 37 27.3 44 22.4 30 30 46.9 38.5 60.8 50.9 40.5 66.3 32.9 69.5 43.6 30.8 40.5 75.4 31.5 53.8 73.9 53.4 25.1 32.2 69.5 38.5 36.5 60.3 43.1 40.5 15.8 48.9 56 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 = The…
- You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01. Ho:μ=67.6Ho:μ=67.6 Ha:μ<67.6Ha:μ<67.6You believe the population is normally distributed. You obtain a sample mean of 64.2 and a sample standard deviation of 10.4 for a sample of size 34.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 =You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01. Ho:μ1=μ2Ho:μ1=μ2 Ha:μ1<μ2Ha:μ1<μ2You obtain the following two samples of data. Sample #1 Sample #2 52 60.1 61.7 56.9 52 59.7 45 49.9 71.9 31.1 47.1 56.1 54.9 45 85.1 67 66.1 51.2 87.2 50.7 73.1 43.3 65.2 58.5 50.3 71.3 60.5 48 62.2 78.6 50.7 56.5 37.8 45.6 41.5 58.5 54.9 76.8 62.6 29.5 71.3 83.5 71.3 64.3 63 74.5 76.8 50.7 78.6 59.3 31.1 54.9 61.2 50.3 75.1 72.3 68.5 85.7 63.3 50.3 79.1 73.5 65.2 58.4 62.3 57 52.9 72.3 88.2 57.4 75.8 68.5 84.1 45 60 79.7 58.1 56.6 77.1 60.9 68.5 67.3 62 45 66.4 79.7 53.5 52.9 79.7 63.5 67.1 74.8 53.5 66.1 68.7 64.2 72.3 55.2 75.5 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…2. Using the t-distribution table in Appendix 2, with a significance level a = 0.05, determine the suitable critical value for conducting the hypothesis test for the Elie's research. Appendix 2 One-tailed test 1 t Two-tailed test df 0.1 0.05 0.025 0.02 0.01 99 1.2902 1.6604 1.9842 2.0812 2.3646 100 1.2901 1.6602 1.9840 2.0809 2.3642 101 1.2900 1.6601 1.9837 2.0806 2.3638
- Under what circumstances is a t statistic used instead of a z-score for a hypothesis test? Justin wants to know whether a commonly prescribed drug does improve the attention span of students with attention deficit disorder (ADD). He knows that the mean attention span for students with ADD who are not taking the drug is 2.3 minutes long. His sample of 12 students taking the drug yielded a mean of 4.6 minutes. Justin can find no information regarding σx , so he calculated s2x =1.96. Determine the critical region using a one-tailed test with alpha = .05. Conduct the hypothesis test (Do the math and compare the t-critical and t-obtained values). State your conclusions in terms of H0 (Should you reject the H0 or fail to reject/accept the H0). Based on your analysis, is there a relationship between the drug and attention span?7) You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01. Ho:μ=66.2Ho:μ=66.2 Ha:μ>66.2Ha:μ>66.2You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=16n=16 with mean M=81.5M=81.5 and a standard deviation of SD=19.1SD=19.1.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... PICK ONE less than (or equal to) αα greater than αα This test statistic leads to a decision to... PICK ONE reject the null accept the null fail to reject the null As such, the final conclusion is that... PICK ONE There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 66.2. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater…Question 4 く Test the claim that the mean GPA of night students is larger than the mean GPA of day students at the .01 significance level. The null and alternative hypothesis would be: Ho:PN = PD Ho:HN H1:PN > PD H1:µN > HD H1:PN < PD H1:PN # PD H1:µN < HD H1:µN # µD HD Ho:PN = PD Ho:PN = pD Ho:HN = HD Ho:UN = D The test is: two-tailed left-tailed right-tailed The sample consisted of 70 night students, with a sample mean GPA of 2.22 and a standard deviation of 0.03, and 50 day students, with a sample mean GPA of 2.21 and a standard deviation of 0.02. The test statistic is: (to 2 decimals) The critical value is: (to 2 decimals) Based on this we: O Reject the null hypothesis O Fail to reject the nul hypothesis