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Medical researchers are interested in determining the relative effectiveness of two drug treatments on patients with a chronic mental illness. Treatment 1 has been around for many years, while treatment 2 has recently been developed based on the latest research. The researchers chose two independent test groups. The first group had 11 patients, all of whom received treatment 1 and had a mean time until remission of 170 days, with a standard deviation of 8 days. The second group had 8 patients, all of whom received treatment 2 and had a mean time until remission of 160 days, with a standard deviation of 9 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Can we conclude, at the 0.05 level of significance, that μ₁, the mean number of days until remission after treatment 1, is greater than μ₂, the mean number of days until remission after treatment 2? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. μ O р X S HO H₁ :0 P (b) Determine the type of test statistic to use. (Choose one) ▼ ロ=ロ 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0#0 OO 0 S ? (d) Find the p-value. (Round to three or more decimal places.) (e) Can we conclude that the mean number of days before remission after treatment 1 is greater than the mean number of days before remission after treatment 2? O Yes O No X OSO

Medical researchers are interested in determining the relative effectiveness of two drug treatments on patients with a chronic mental illness. Treatment 1 has been around for many years, while treatment 2 has recently been developed based on the latest research. The researchers chose two independent test groups. The first group had 11 patients, all of whom received treatment 1 and had a mean time until remission of 170 days, with a standard deviation of 8 days. The second group had 8 patients, all of whom received treatment 2 and had a mean time until remission of 160 days, with a standard deviation of 9 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Can we conclude, at the 0.05 level of significance, that μ₁, the mean number of days until remission after treatment 1, is greater than μ₂, the mean number of days until remission after treatment 2? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. μ O р X S HO H₁ :0 P (b) Determine the type of test statistic to use. (Choose one) ▼ ロ=ロ 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0#0 OO 0 S ? (d) Find the p-value. (Round to three or more decimal places.) (e) Can we conclude that the mean number of days before remission after treatment 1 is greater than the mean number of days before remission after treatment 2? O Yes O No X OSO

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Medical researchers are interested in determining the relative effectiveness of two drug treatments on patients with a chronic mental illness. Treatment 1 has been around for many years, while treatment 2 has recently been developed based on the latest research. The researchers chose two independent test groups. The first group had 11 patients, all of whom received treatment 1 and had a mean time until remission of 170 days, with a standard deviation of 8 days. The second group had 8 patients, all of whom received treatment 2 and had a mean time until remission of 160 days, with a standard deviation of 9 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Can we conclude, at the 0.05 level of significance, that µ₁, the mean number of days until remission after treatment 1, is greater than μ₂, the mean number of days until remission after treatment 2? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. μ Р X Â Ho : H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ 0=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) 0#0 (d) Find the p-value. (Round to three or more decimal places.) (e) Can we conclude that the mean number of days before remission after treatment 1 is greater than the mean number of days before remission after treatment 2? O Yes O No X a □<ロ 3 030 O>O ?
Transcribed Image Text:Medical researchers are interested in determining the relative effectiveness of two drug treatments on patients with a chronic mental illness. Treatment 1 has been around for many years, while treatment 2 has recently been developed based on the latest research. The researchers chose two independent test groups. The first group had 11 patients, all of whom received treatment 1 and had a mean time until remission of 170 days, with a standard deviation of 8 days. The second group had 8 patients, all of whom received treatment 2 and had a mean time until remission of 160 days, with a standard deviation of 9 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Can we conclude, at the 0.05 level of significance, that µ₁, the mean number of days until remission after treatment 1, is greater than μ₂, the mean number of days until remission after treatment 2? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. μ Р X Â Ho : H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ 0=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) 0#0 (d) Find the p-value. (Round to three or more decimal places.) (e) Can we conclude that the mean number of days before remission after treatment 1 is greater than the mean number of days before remission after treatment 2? O Yes O No X a □<ロ 3 030 O>O ?
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