In: Statistics and Probability
Can you please answer the following question
Fifty cities provided information on vacancy rates (in percent) in local apartments in the following frequency distribution. The sample mean and the sample standard deviation are 9% and 3.6%, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table)
Vacancy Rate | Frequency | |||
Less than 6 | 10 | |||
6 up to 9 | 10 | |||
9 up to 12 | 20 | |||
12 or more | 10 | |||
a. Apply the goodness-of-fit test for normality at the 5% significance level. Do the sample data suggest that vacancy rates do not follow the normal distribution? First, select the appropriate null and alternative hypotheses.
H_{0}: Vacancy rates are not normally distributed with a mean of 9% and a standard deviation of 3.6%.; H_{A}: Vacancy rates are normally distributed with a mean of 9% and a standard deviation of 3.6%.
H_{0}: Vacancy rates are normally distributed with a mean of 9% and a standard deviation of 3.6%.; H_{A}: Vacancy rates are not normally distributed with a mean of 9% and a standard deviation of 3.6%.
b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
c. Find the p-value.
p-value < 0.01
0.01 ≤ p-value < 0.025
0.025 ≤ p-value < 0.05
0.05 ≤ p-value < 0.10
p-value ≥ 0.10
d. What is the conclusion?
Reject H_{0}; there is not enough evidence to support the claim that the vacancy rates are not normally distributed.
Reject H_{0}; there is enough evidence to support the claim that the vacancy rates are not normally distributed.
Do not reject H_{0}; there is not enough evidence to support the claim that the vacancy rates are not normally distributed.
Do not reject H_{0}; there is enough evidence to support the claim that the vacancy rates are not normally distributed.