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 ______
A)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.
B)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.
C)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.
D)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.

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula for a one-sample t-test, which compares the sample mean to a known value (in this case, $3,300) while accounting for the sample's standard deviation and size. When the absolute value of the test statistic exceeds the absolute value of the critical value (determined by the significance level α = 0.05 and the degrees of freedom, which would be 11 for a sample size of 12), it indicates that the observed sample mean ($3,690) is significantly different from the hypothesized mean ($3,300). Therefore, we can reject the null hypothesis and conclude that the average monthly rate is not equal to $3,300.

Medicare Would Like to Test the Hypothesis That the Average