Medicare would like to test the hypothesis that the average monthly rate for a one-bedroom assisted-living facility is equal to $3,300. A random sample of 12 assisted-living facilities had an average rate of $3,690 per month. The standard deviation for this sample was $530. Medicare would like to set α = 0.05. Note: Two hypotheses for the test are H0: μ = $3,300 vs H1: μ ≠ $3,300, and it is a two-tailed test.
Calculate the test statistic, find the critical values, and mark them on the corresponding curve. Mark the rejection regions. Would you reject the null hypothesis? Give the reason for your decision.