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 p-value for this hypothesis test would be between ________.
a) 0.01 and 0.025
b) 0.025 and 0.05
c) 0.005 and 0.01
d) 0.001 and 0.005

Answer 1

The question requires performing a one-sample t-test to find the p-value for Medicare's hypothesis that the average monthly rate for one-bedroom assisted-living facilities is $3,300. The sample data suggest a different average, and the p-value would indicate how strongly the sample evidence contradicts the hypothesized mean.

Step-by-step explanation:

The question is asking to determine the p-value of a hypothesis test, where Medicare wants to test if the average monthly rate for a one-bedroom assisted-living facility is equal to $3,300 against the alternative that the actual average rate differs from this amount.

Given a sample mean of $3,690, a standard deviation of $530, and a sample size of 12, we need to conduct a one-sample t-test to compare the sample mean to the population mean of $3,300. Using the significance level α = 0.05, if we were to perform this statistical test, we would calculate the t-statistic and then use the t-distribution to find the p-value. Based on the information provided in the question, the p-value appears to be very small, suggesting that the sample provides strong evidence against the null hypothesis.

The correct range for the p-value would need to be found by performing the calculations using the appropriate statistical methods or software.