Medical researchers interested in determining the relative effectiveness of two different drug treatments on people with a chronic mental illness established two independent test groups. The first group consisted of 7 people with the illness, and the second group consisted of 12 people with the illness. The first group received treatment 1 and had a mean time until remission of 199 days, with a standard deviation of 6 days. The second group received treatment 2 and had a mean time until remission of 187 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 0.01 level of significance, that the mean number of days before remission after treatment 1, μ1, is greater than the mean number of days before remission after treatment 2, μ2? Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
Null Hypothesis: ?
Alternative Hypothesis: ?
Type of test statistic: ? (z, t, chi square, F)
The value of the test statistic: ? (round to 3 decimal places)
The P-value: ? (round to 3 decimal places)
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?