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 alphaequals0.05. The​ p-value for this hypothesis test would be between​ _______.

Answer 1

Given that average monthly rate for​ one-bedroom assisted-living facility is equal to​ $3,300

So Population mean = 3300

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

So Sample mean = 3690

Sample Standard Deviation S = 530

Sample size n = 12

Medicare would like to test the hypothesis that the average monthly rate for​ one-bedroom assisted-living facility is equal to​ $3,300

Null Hypothesis H₀ : = 3300

Alternate Hypothesis H₀ : 3300

The Null Hypothesised value is ₀ = 3300

Here we use one sample t-test since n is less than 30 and distribution is assumed to be normal

t-test statistic = ( - ₀) / (S / )

= (3690 - 3300) / (530 / )

= 390 / (530 / 3.464102)

= 390 / 152.9978

= 2.549056

Given significance level = 0.05

Number of degrees of freedom = n - 1

= 11

The p-value for a t-score of 2.549056 and 11 degrees of freedom for a two-tailed test = 0.02704

Since the p-value is less than the significance level, we reject the Null Hypothesis H₀ and conclude that there is enough evidence at 0.05 significance level to claim that the average monthly rate for​ one-bedroom assisted-living facility is not equal to​ $3,300