Question

In: Statistics and Probability

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002. Ho:μ1=μ2Ho:μ1=μ2 H1:μ1≠μ2H1:μ1≠μ2...

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002.

Ho:μ1=μ2Ho:μ1=μ2
H1:μ1≠μ2H1:μ1≠μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=19n1=19 with a mean of M1=77.6M1=77.6 and a standard deviation of SD1=20.7SD1=20.7 from the first population. You obtain a sample of size n2=20n2=20 with a mean of M2=72.1M2=72.1 and a standard deviation of SD2=8.7SD2=8.7 from the second population.

2a. What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

2b. What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

2c. The test statistic is...

A. in the critical region

B. not in the critical region

2d. This test statistic leads to a decision to...

A. reject the null

B. accept the null

C. fail to reject the null

2e. As such, the final conclusion is that...

A. There is sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean.

B. There is not sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean.

C. The sample data support the claim that the first population mean is not equal to the second population mean.

D. There is not sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean.

Expert Solution

Solution

2a. What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =3.468

2b. What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic

2c. The test statistic is...

B. not in the critical region

2d. This test statistic leads to a decision to...

C. fail to reject the null

2e. As such, the final conclusion is that..

D. There is not sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean.

orchestra answered 2 years ago

You wish to test the following claim (H1H1) at a significance level of α=0.001α=0.001. Ho:μ1=μ2Ho:μ1=μ2 H1:μ1≠μ2H1:μ1≠μ2...

You wish to test the following claim (H1H1) at a significance level of α=0.001α=0.001. Ho:μ1=μ2Ho:μ1=μ2 H1:μ1≠μ2H1:μ1≠μ2 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=24n1=24 with a mean of M1=85.8M1=85.8 and a standard deviation of SD1=19.3SD1=19.3 from the first population. You obtain a sample of size n2=17n2=17 with...

You wish to test the following claim (H1H1) at a significance level of α=0.02α=0.02. Ho:μ1=μ2Ho:μ1=μ2 H1:μ1>μ2H1:μ1>μ2...

You wish to test the following claim (H1H1) at a significance level of α=0.02α=0.02. Ho:μ1=μ2Ho:μ1=μ2 H1:μ1>μ2H1:μ1>μ2 You obtain the following two samples of data. Sample #1 Sample #2 97.7 78.7 14.7 91.3 90.1 39.8 56.9 47.2 67.5 62.3 64.9 26.7 79.4 52.9 63.3 69.1 20.4 67.5 54.1 67 46.4 52.3 44.2 65.9 95.8 56.9 78.7 85.9 56.4 59.1 53.5 72.5 70.8 61.2 64.9 70.2 68.6 44.2 41.6 77.4 81.6 14.7 55.2 71.4 56.4 50.5 52.9 41.6 24 49.9 53.5 74.9...

You wish to test the following claim (H1) at a significance level of α=0.002. Ho:μ1=μ2 H1:μ1≠μ2...

You wish to test the following claim (H1) at a significance level of α=0.002. Ho:μ1=μ2 H1:μ1≠μ2 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=11 with a mean of M1=63.8 and a standard deviation of SD1=12.9 from the first population. You obtain a sample of size n2=18 with...

You wish to test the following claim (Ha) at a significance level of α=0.002. Ho:μ1=μ2 Ha:μ1<μ2...

You wish to test the following claim (Ha) at a significance level of α=0.002. Ho:μ1=μ2 Ha:μ1<μ2 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=18 with a mean of M1=59.3 and a standard deviation of SD1=15.2 from the first population. You obtain a sample of size n2=13 with...

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002. Ho:μ=57.7Ho:μ=57.7 H1:μ≠57.7H1:μ≠57.7...

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002. Ho:μ=57.7Ho:μ=57.7 H1:μ≠57.7H1:μ≠57.7 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=98n=98 with mean M=60.9M=60.9 and a standard deviation of SD=7.7SD=7.7. 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? (Report answer accurate to four decimal places.) p-value...

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002. Ho:μ=75.1Ho:μ=75.1 H1:μ>75.1H1:μ>75.1...

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002. Ho:μ=75.1Ho:μ=75.1 H1:μ>75.1H1:μ>75.1 You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 77 87.3 81.7 96.8 113.2 82.2 81.2 84.6 4a. What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = 4b. What is the test statistic for this sample? (Report answer accurate to three...

You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. For the...

You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. For the context of this problem, μd=PostTest−PreTestμd=PostTest-PreTest where the first data set represents a pre-test and the second data set represents a post-test. (Each row represents the pre and post test scores for an individual. Be careful when you enter your data and specify what your μ1μ1 and μ2μ2 are so that the differences are computed correctly.) Ho:μd=0Ho:μd=0 Ha:μd≠0Ha:μd≠0 You believe the population of difference scores...

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. Ho:μ1=μ2Ho:μ1=μ2 Ha:μ1<μ2Ha:μ1<μ2...

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. Ho:μ1=μ2Ho:μ1=μ2 Ha:μ1<μ2Ha:μ1<μ2 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=12n1=12 with a mean of M1=71.3M1=71.3 and a standard deviation of SD1=11.6SD1=11.6 from the first population. You obtain a sample of size n2=25n2=25 with...

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>μ2...

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>μ2 You obtain the following two samples of data. Sample #1 Sample #2 76.6 68.8 83.7 70.2 82.1 89.6 76.6 83.7 78.4 72.8 79.7 76.6 85.6 80.6 81.2 74.9 77.3 77.8 77.3 85.9 65.4 79.7 73.6 73.6 78.5 79 66.6 76.1 77.7 79 81.1 74.7 83.9 77.7 80.6 86.1 74.7 81.4 77.3 91.8 71.3 81.4 77.3 75.1 82.1 89.6 81.6 56.1 67.4 76.7 84.6 85.9...

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<μ2...

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<μ2 You obtain the following two samples of data. Sample #1 Sample #2 28 70.9 54 62.1 46.2 64 48.4 49.5 44.2 52.3 57.3 55.5 76.6 33.7 39.6 67.3 68.6 55.1 51.6 53 62.1 64.5 58.4 76.6 49.1 42.9 41.1 54.8 60.4 73.9 46.2 43.4 43.8 46.2 40.6 46.2 28 41.1 26.2 41.1 30.7 47.3 60 29.4 49.5 44.2 52 43.8 54.8 40.1 37.9 71.9...