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. Which one of the following statements is true?
A)Because the p-value is greater than α, we fail to reject the null hypothesis and cannot conclude that the average monthly rate for an assisted-living facility is not equal to $3,300.
B)Because the p-value is less than α, we reject the null hypothesis and conclude that the average monthly rate for an assisted-living facility is not equal to $3,300.
C)Because the p-value is greater than α, we fail to reject the null hypothesis and conclude that the average monthly rate for an assisted-living facility is equal to $3,300.
D)Because the p-value is less than α, we fail to reject the null hypothesis and conclude that the average monthly rate for an assisted-living facility is not equal to $3,300.

Question

Quizplus · Accepted Answer

Given the sample mean is significantly higher than the hypothesized mean ($3,690 vs. $3,300), and assuming normal distribution and sufficient sample size for the Central Limit Theorem to apply, the likelihood of observing such a sample mean if the true mean were indeed $3,300 would be low, leading to a small p-value. If the p-value is less than the significance level (α = 0.05), it suggests that the observed difference is statistically significant, and thus, we reject the null hypothesis that the average monthly rate is equal to $3,300.

Medicare Would Like to Test the Hypothesis That the Average