Question

Medicare would like to test the hypothesis that the average monthly rate for 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. The conclusion for this hypothesis test would be that because the absolute value of the test statistic is

		less than the absolute value of the critical value, we cannot conclude that the average monthly rate for an assisted-living facility is not equal to $3,300.
		more than the absolute value of the critical value, we cannot conclude that the average monthly rate for an assisted-living facility is not equal to $3,300.
		more than the absolute value of the critical value, we can conclude that the average monthly rate for an assisted-living facility is not equal to $3,300.
		less than the absolute value of the critical value, we can conclude that the average monthly rate for an assisted-living facility is not equal to $3,300.

Answer 1

Excel add-in (PH Stat) procedure: Step 1: In EXCEL, Select Add-Ins > PH Stat > One-Sample Tests > t Test for the mean, Sigma unknown. Step 2: Enter 3300 under Null hypothesis. Step 3: Enter 0.05 under Level of significance. Step 4: In Sample Statistic Options, choose Sample Statistic Known and enter 12 as the Sample size and 3690 as the Sample mean, and 530 as the Sample standard deviation. Step 5: In Test Options, choose Two Tail Test. Step 6: Click OK Excel add-in (PH Stat) output:

t Test for Hypothesis of the Mean Data Null Hypothesis = Level of Significance Sample Size Sample Mean Sample Standard Deviation 3300 0.05 12 3690 530 Intermediate Calculations Standard Error of the Mean 152.9978 Degrees of Freedom 11 t Test Statistic 2.5491 -2.2010 Two-Tail Test Lower Critical Value Upper Critical Value p-Value Reject the null hypothesis 2.2010 0.0270 The value of the test statistic is t = 2.549. Conclusion:

Since t(= 2.549) > 2.201, then reject the null hypothesis. Correct Answer: The conclusion for this hypothesis test would be that because the absolute value of the test statistic is more than the absolute value of the critical value, we can conclude that the average monthly rate for an assisted-living facility is not equal to $3,300.