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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 171 days, with a standard deviation of 8 days. The second group had 9 patients, all of whom received treatment 2 and had a mean time until remission of 166 days, with a standard deviation of 6 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 until remission after treatment 1, is greater than ,, 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 H. 2. H : 0 H : I DO (b) Determine the type of test statistic to use. 0=0 OSO 020 (Choose one) V (c) Find the value of the test statistic. (Round to three or more decimal places.) *0 00 C X (d) Find the p-value. (Round to three or more 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? Yes No