For each of the following samples that were given an experimental treatment, test whether the samples represent populations that are different from the generalpopulation: (a) a sample of 11 with a mean of 41, (b) a sample of 1 with a mean of 47. The general population of individuals has a mean of 38, a standard deviation of7, and follows a normal curve. For each sample, carry out a Z test using the five steps of hypothesis testing with a two-tailed test at the 0.05 significance level, andmake a drawing of the distributions involved. (c) Figure the 95% confidence interval for parts (a) and (b).Click here to view page 1 of the table. Click here to view. page 2 of the table. Click here to view.page 3 of the table. Click here to view page 4 of the table.(a) Determine a research hypothesis and a null hypothesis. Choose the correct answer below.O A. The research hypothesis is the means of the populations are the same. The null hypothesis is the mean of the general population is less than the mean of thesample population.O B. The research hypothesis is the means of the populations are the same. The null hypothesis is the means of the populations are not the same.OC. The research hypothesis is the means of the populations are not the same. The null hypothesis in the means of the populations are the same.OD. The research hypothesis is the mean of the sample population is less than the general population. The null hypothesis is the moan of the general population isless than the sample population.Assume that the distribution of means is approximately normal. What are the cutoff sample scores on the comparison distribution at which the null hypothesis should berejected?(Type integers or decimals rounded to two decimal places as needed. Use a comma to separate answers as needed)Determine the sample's Z score on the comparison distribution.z-(Type an integer or a decimal rounded to two decimal places as needed.)Decide whether to reject the null hypothesis. Explain. Choose the correct arnswer below.A. The sample score is extreme enough to rejoct the null hypothesis. The resoarch hypothesis in false.B. The sample score is not extreme enough to reject the null hypothesis. The experiment is inconclusive.OC. The sample score is not extreme enough to reject the null hypothesis. The research hypothesis is true. OD. The sample score is extreme enough to reject the null hypothesis. The research hypothesis is supported.Make a drawing of the distributions. The distribution of the general population is in blue and the distribution of means is in black. Choose the correct answer below.OA.OB.Oc.OD.(b) Determine a research hypothesis and a null hypothesis. Choose the correct answer below.OA The research hypothesis is the means of the populations are the same. The null hypothesis is the means of the populations are not the same.B. The research hypothesis is the means of the populations are the same. The null hypothesis is the mean of the general population is less than the mean of thesample population.OC. The research hypothesis is the means of the populations are not the same. The null hypothesis is the means of the populations are the same.OD. The research hypothesis is the mean of the sample population is less than the general population. The nul hypothesis is the mean of the general population isless than the sample population.Assume that the dastribution of means is approximately nomal. Use the cutoff sample score on the comparison distribution at which the null hypothesis should berejocted from part (a). Determine the samplo's Z score on the comparison distribution.z-Type an integer or a decimal rounded to two decimal places as needed)Decide whether to reject the null hypothesis. Explain. Choose the correct answor belowDecide whether to reject the null hypothesis. Explain. Choose the corect answer below.OA The sample score is extreme enough to reject the null hypothesis. The research hypothesis is false.B. The sample score is not extreme enough to reject the null hypothesis. The research hypothesis is true.C. The sample score is not extreme enough to reject the null hypothesis. The experiment is inconclusive.OD. The sample score is extreme enough to reject the null hypothesis. The research hypothesis is supported.Make a drawing of the comparison distribution. Choose the correct answer below.OA.O B.Oc.OD.1837(c) Figure the 95% confidence interval for part (a).One can be 95% confident that the true population mean is between and(Type integers or decimais rounded to two decimal places as needed.)Figure the 95% confidence interval for part (b).One can be 95% confident that the true population mean is between and(Type integers or decimals rounded to two decimal places as needed.)

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Given information:
μ=38, σ=7Sample a) n=11, x¯=41Sample b) n=1, x¯=47