Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether μ1>μ2 at the α=0.10 level of significance for the given sample data. (b) Construct a90%confidence interval aboutμ1−μ2 Population 1 Population 2 n 26 21 x 46.9 41.3 s 6.9 13.1
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Step by step
Solved in 3 steps with 2 images
- You wish to test the following claim (H1H1) at a significance level of α=0.10α=0.10. Ho:μ=66.8Ho:μ=66.8 H1:μ>66.8H1:μ>66.8You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: data 44.5 103.2 74.3 72.1 50.6 63.6 52.2 68.5 29.6 What is the critical value for this test? (Report answer accurate to four decimal places.) critical value = What is the test statistic for this sample? (Report answer accurate to four 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... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 66.8. There is not sufficient evidence to warrant rejection of the claim that the population mean…This one was giving me problems. How do I know the difference between Ha and Ho and when to accept and reject?Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα/2, (b) find the critical value zα/2, or (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n=192, x=33.7 hg, s=6.7 hg. The confidence level is 90%. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- Use the given statistics to complete parts (a) and (b). Assume that the populations are normally distributed. (a) Test whether μ1>μ2 at the α=0.01 level of significance for the given sample data. (b) Construct a 99% confidence interval about μ1−μ2. Population 1 Population 2 n 23 20 x 47.2 44.6 s 6.8 10.7 (a) Identify the null and alternative hypotheses for this test. A. H0: μ1≠μ2 H1: μ1=μ2 B. H0: μ1=μ2 H1: μ1≠μ2 C. H0: μ1=μ2 H1: μ1<μ2 D. H0: μ1>μ2 H1: μ1=μ2 E. H0: μ1=μ2 H1: μ1>μ2 Your answer is correct. F. H0: μ1<μ2 H1: μ1=μ2 Find the test statistic for this hypothesis test.You wish to test the following claim (Ha) at a significance level of α=0.01. H0:μ1≤μ2Ha:μ1>μ2 You believe both populations are normally distributed, but you do not know the standard deviations for either. You obtain a sample of size n1=18 with a mean of M1=54.9 and a standard deviation of SD 1=7.9. You obtain a sample of size n2=17 with a mean of M2=48.5 and a standard deviation of SD2=18.9. test statistic = p-value = The p-value is...A.less than (or equal to) αB. greater than α This test statistic leads to a decision to...A. reject the null hypothesisB. fail to reject the null hypothesis As such, the final conclusion is that...A. There is sufficient sample evidence to support the claim that the first population mean is greater than the second population mean.B. There is not sufficient sample evidence to support the claim that the first population mean is greater than the second population mean.ssume that both populations are normally distributed. (a) Test whether μ1≠μ2 at the α=0.05 level of significance for the given sample data. (b) Construct a 95% confidence interval about μ1−μ2. Population 1 Population 2 n 14 14 x 19.1 20.4 s 4.2 4.8
- You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. Ho:μ=57.8Ho:μ=57.8 Ha:μ<57.8Ha:μ<57.8 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=6n=6 with mean ¯x=50.2x¯=50.2 and a standard deviation of s=9.8s=9.8. What is the test statistic for this sample? test statistic = Round to 3 decimal places What is the p-value for this sample? p-value = Use Technology Round to 4 decimal places. The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is less than 57.8. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 57.8. The sample data support the claim that the…Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα/2, (b) find the critical value zα/2, or (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n=167, x=28.2 hg, s=6.2 hg. The confidence level is 95%. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. tα/2= nothing (Round to two decimal places as needed.) B. zα/2= nothing (Round to two decimal places as needed.) C. Neither the normal distribution nor the t distribution applies.It is crucial that the variance of a production process be less than or equal to 25. A sample of 22 is taken. The sample variance equaled 26. a. Construct a 90% confidence interval for the population variance. b. Construct a 90% confidence interval for the population standard deviation. c. Test at 10% level of significance that whether the variance of the production process exceeds its standard. (Use the critical value approach.) (You must state H0 and Ha, compute the test statistic, report the critical value, and draw conclusion.)
- 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…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…Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα/2, (b) find the critical value zα/2, or (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn girls: n=236, x=31.6 hg, s=6.9 hg. The confidence level is 90%.
