Question

In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $108.50. Let the population standard deviation of room price be $16.

            a. (6 points) Formulate the hypotheses to determine whether or not the average room price is significantly different from $112.

            b.   (7 points) Compute the test statistic.

            c.   (7 points) At 99% confidence using the p-value approach, test the hypotheses.

Answer 1

a) H₀ : µ = 112

H₁ : µ ≠ 112

b) test statistic = (sample mean - µ) / (sd / sqrt(n)) = (108.50 - 112) / (16/sqrt(64)) = -1.75

c) p-value = 2 * P(Z < -1.75) = 2 * 0.0401 = 0.0802

Since p-value is not less than 0.01, we should not reject the null hypothesis