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 12 patients, all of whom received treatment 1 and had a mean time until remission of 169 days, with a standard deviation of 8 days. The second group had 10 patients, all of whom received treatment 2 and had a mean time until remission of 167 days, with a standard deviation of 5 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