A clinical psychologist wants to choose between two treatment methods. She randomly selects 3 patients to...

  

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A clinical psychologist wants to choose between two treatment methods. She randomly selects 3 patients to receive Therapy 1 and 3 patients to receive Therapy 2. After 1 month of treatment, their improvement is scored on a numeric scale, with a higher number implying greater improvement. The scores are given below. The null hypothesis is Ho: ₁2. Assume equal population standard deviations. Complete parts a through c below. Therapy 1:27, 47, 45 Therapy 2: 10, 20, 30 a. Determine the mean of Therapy 1, the mean of Therapy 2, the pooled standard deviation, the standard error of (x₁-x₂), the degrees of freedom, and the values of a 95% confidence interval for the mean difference. First determine the mean of Therapy 1, X₁. x₁ = (Type an integer or decimal rounded to one decimal place as needed.) Determine the mean of Therapy 2, X₂. x₂ = (Type an integer or decimal rounded to one decimal place as needed.) Determine the degrees of freedom, df. df= Determine the values of a 95% confidence interval for the mean difference. The 95% confidence interval is. (Round to two decimal places as needed.) b. Explain how to interpret the confidence interval. Why is it so wide? Interpret the confidence interval. Choose the correct answer below. A clinical psychologist wants to choose between two treatment methods. She randomly selects 3 patients to receive Therapy 1 and 3 patients to receive Therapy 2. After 1 month of treatment, their improvement is scored on a numeric scale, with a higher number implying greater improvement. The scores are given below. The null hypothesis is Ho: H₁ H₂. Assume equal population standard deviations. Complete parts a through c below. Therapy 1: 27, 47, 45 Therapy 2: 10, 20, 30 b. Explain how to interpret the confidence interval. Why is it so wide? Interpret the confidence interval. Choose the correct answer below. A. The psychologist can be 95% confident that the true population mean difference between the mean scores for Therapy 1 and Therapy 2 is either less than the lower bound or greater than the upper bound of the confidence interval. OB. The psychologist can be 95% confident that the true population mean between the mean scores for Therapy 1 and Therapy 2 is between the lower and upper bounds of the confidence interval. OC. The psychologist can be 95% confident that the true population mean difference between the mean scores for Therapy 1 and Therapy 2 is between the lower and upper bounds of the confidence interval. Why is it so wide? Choose the correct answer below. OA. The confidence interval is wide because the confidence level is very large. OB. The confidence interval is wide because the two samples sizes are very small. OC. The confidence interval is wide because the difference between the two sample means is very large. OD. The confidence interval is wide because the two samples sizes are equal. c. When the sample sizes are very small, it may be worth sacrificing some confidence to achieve more precision. Determine a 90% confidence interval. At this confidence level, can it be concluded that Therapy 1 is better? The 90% confidence interval is ( (Round to two decimal places as needed.) At this confidence level, can it be concluded that Therapy 1 is better? OA. Since the interval does not contain 0 and all the values in the interval are negative, Therapy 1 is not better than Therapy 2. OB. Since the interval does not contain 0 and all the values in the interval are positive, Therapy 1 is not better than Therapy 2. OC. Since the interval does not contain 0 and all the values in the interval are positive, it is plausible that Therapy 1 is better than Therapy 2. D. Since the interval does not contain 0 and all the values in the interval are negative, it is plausible that Therapy 1 is better than Therapy 2. A clinical psychologist wants to choose between two treatment methods. She randomly selects 3 patients to receive Therapy 1 and 3 patients to receive Therapy 2. After 1 month of treatment, their improvement is scored on a numeric scale, with a higher number implying greater improvement. The scores are given below. The null hypothesis is Ho: ₁2. Assume equal population standard deviations. Complete parts a through c below. Therapy 1:27, 47, 45 Therapy 2: 10, 20, 30 a. Determine the mean of Therapy 1, the mean of Therapy 2, the pooled standard deviation, the standard error of (x₁-x₂), the degrees of freedom, and the values of a 95% confidence interval for the mean difference. First determine the mean of Therapy 1, X₁. x₁ = (Type an integer or decimal rounded to one decimal place as needed.) Determine the mean of Therapy 2, X₂. x₂ = (Type an integer or decimal rounded to one decimal place as needed.) Determine the degrees of freedom, df. df= Determine the values of a 95% confidence interval for the mean difference. The 95% confidence interval is. (Round to two decimal places as needed.) b. Explain how to interpret the confidence interval. Why is it so wide? Interpret the confidence interval. Choose the correct answer below. A clinical psychologist wants to choose between two treatment methods. She randomly selects 3 patients to receive Therapy 1 and 3 patients to receive Therapy 2. After 1 month of treatment, their improvement is scored on a numeric scale, with a higher number implying greater improvement. The scores are given below. The null hypothesis is Ho: H₁ H₂. Assume equal population standard deviations. Complete parts a through c below. Therapy 1: 27, 47, 45 Therapy 2: 10, 20, 30 b. Explain how to interpret the confidence interval. Why is it so wide? Interpret the confidence interval. Choose the correct answer below. A. The psychologist can be 95% confident that the true population mean difference between the mean scores for Therapy 1 and Therapy 2 is either less than the lower bound or greater than the upper bound of the confidence interval. OB. The psychologist can be 95% confident that the true population mean between the mean scores for Therapy 1 and Therapy 2 is between the lower and upper bounds of the confidence interval. OC. The psychologist can be 95% confident that the true population mean difference between the mean scores for Therapy 1 and Therapy 2 is between the lower and upper bounds of the confidence interval. Why is it so wide? Choose the correct answer below. OA. The confidence interval is wide because the confidence level is very large. OB. The confidence interval is wide because the two samples sizes are very small. OC. The confidence interval is wide because the difference between the two sample means is very large. OD. The confidence interval is wide because the two samples sizes are equal. c. When the sample sizes are very small, it may be worth sacrificing some confidence to achieve more precision. Determine a 90% confidence interval. At this confidence level, can it be concluded that Therapy 1 is better? The 90% confidence interval is ( (Round to two decimal places as needed.) At this confidence level, can it be concluded that Therapy 1 is better? OA. Since the interval does not contain 0 and all the values in the interval are negative, Therapy 1 is not better than Therapy 2. OB. Since the interval does not contain 0 and all the values in the interval are positive, Therapy 1 is not better than Therapy 2. OC. Since the interval does not contain 0 and all the values in the interval are positive, it is plausible that Therapy 1 is better than Therapy 2. D. Since the interval does not contain 0 and all the values in the interval are negative, it is plausible that Therapy 1 is better than Therapy 2.