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 10 patients, all of whom received treatment 1 and had a mean time until remission of 165 days, with a standard deviation of 6 days. The second group had 7 patients, all of whom received treatment 2 and had a mean time until remission of 163 days, with a standard deviation of 8 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 H, and the alternative hypothesis H₁. Ho :0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) V (c) Find the value of the test statistic. (Round to three or more decimal places.) 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? Yes No 3 |x a X S 00 0-0 ≤0 20 >O

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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 10 patients, all of whom received treatment 1 and had a mean time until remission of 165 days, with a standard
deviation of 6 days. The second group had 7 patients, all of whom received treatment 2 and had a mean time until remission of 163 days, with a
standard deviation of 8 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 H. and the alternative hypothesis H₁.
H₂ : 0
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 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?
Yes No
3
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X
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S
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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 10 patients, all of whom received treatment 1 and had a mean time until remission of 165 days, with a standard deviation of 6 days. The second group had 7 patients, all of whom received treatment 2 and had a mean time until remission of 163 days, with a standard deviation of 8 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 H. and the alternative hypothesis H₁. H₂ : 0 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 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? Yes No 3 X ローロ X O S <D Р OSO 020 S ê >D
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