Medical researchers are interested in determining the relative effectiveness of two drug treatments on patients with a chronic mental illness. Treatment 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 i , 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 H and the alternative hypothesis H P H : I X S p H, : I (b) Determine the type of test statistic to use. (Choose one) 0=0 050 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 00 X (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