Researchers conducted a study to determine whether magnets are effective in treating back pain. The results (higher values indicate larger reductions in pain levels) are shown in the table for the treatment (with magnets) group and the sham (or placebo) group.

treatment sham sample size 19 22

mean 12 10

standard deviation 4 3

Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Use the critical value method and a 0.10 significance level to test the claim that the treatment mean measure of reduction in back pain is equal to the sham mean measure of reduction in back pain. (Hint: Consider statistic_treatment-statistic_sham.)

Enter the smallest critical value. (Round your answer to nearest thousandth.)