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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 13 patients, all of whom received treatment 1 and had a mean time until remission of 178 days, with a standard deviation of 9 days. The second group had 8 patients, all of whom received treatment 2 and had a mean time until remission of 171 days, with a standard deviation of 7 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 0.10 level of significance, that μ₁, the mean number of days until remission after treatment 1, is greater than ₂, 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 H. and the alternative hypothesis H₁. H: D H, D (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the critical value at the 0.10 level of significance. (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? Yes No μ. σ |x X 19 S X □<口 Р 0=0 OSO 20 S O

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 13 patients, all of whom received treatment 1 and had a mean time until remission of 178 days, with a standard deviation of 9 days. The second group had 8 patients, all of whom received treatment 2 and had a mean time until remission of 171 days, with a standard deviation of 7 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 0.10 level of significance, that μ₁, the mean number of days until remission after treatment 1, is greater than ₂, 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 H. and the alternative hypothesis H₁. H: D H, D (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the critical value at the 0.10 level of significance. (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? Yes No μ. σ |x X 19 S X □<口 Р 0=0 OSO 20 S O

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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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 13 patients, all of whom received treatment 1 and had a mean time until remission of 178 days, with a standard deviation of 9 days. The second group had 8 patients, all of whom received treatment 2 and had a mean time until remission of 171 days, with a standard deviation of 7 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 0.10 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 H. and the alternative hypothesis H₁. H: D H₁:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value at the 0.10 level of significance. (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? Yes No μ X 4 □□ O 0=0 Oso X S ô O<O Р 00 020 S 0>0
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 13 patients, all of whom received treatment 1 and had a mean time until remission of 178 days, with a standard deviation of 9 days. The second group had 8 patients, all of whom received treatment 2 and had a mean time until remission of 171 days, with a standard deviation of 7 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 0.10 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 H. and the alternative hypothesis H₁. H: D H₁:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value at the 0.10 level of significance. (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? Yes No μ X 4 □□ O 0=0 Oso X S ô O<O Р 00 020 S 0>0
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