Question

Chapter 12 Homework instructions | help Question 7 (of 7) Save & Exit Submit 7.value: 10.00 points Exercise 12-29 Algo Seventy four 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 10% and 3.6%, respectively. Use Table 3. Vacancy Rate (in percent) Frequency Less than 6 6 6 up to 9 15 9 up to 12 32 12 or more 21 a. Choose the appropriate null and alternative hypotheses. H0: Vacancy rates are normally distributed with a mean of 10% and a standard deviation of 3.6%.; HA: Vacancy rates are not normally distributed with a mean of 10% and a standard deviation of 3.6%. H0: Vacancy rates are not normally distributed with a mean of 10% and a standard deviation of 3.6%.; HA: Vacancy rates are normally distributed with a mean of 10% and a standard deviation of 3.6%. b. Calculate the value of the test statistic at the 10% significance level. (Round the z value to 2 decimal places, all other intermediate values to at least 4 decimal places and final answer to 2 decimal places.) Test statistic c. Approximate the p-value. p-value < 0.010 0.025 Picture p-value < 0.050 0.010 Picture p-value < 0.025 0.050 Picture p-value < 0.100 p-value Picture 0.100 d. What is the conclusion? Do not reject H0; there is enough evidence to support the claim that the vacancy rates are normally distributed Do not reject H0; there is not enough evidence to support the claim that the vacancy rates are not normally distributed Reject H0; there is not enough evidence to support the claim that the vacancy rates are not normally distributed Reject H0; there is enough evidence to support the claim that the vacancy rates are normally distributed e. Do the sample data suggest that vacancy rates do not follow the normal distribution? No Yes

Answer 1

a) Null and alternative hypothesis:

H0: Vacancy rates are normally distributed with a mean of 10% and a standard deviation of 3.6%.;

HA: Vacancy rates are not normally distributed with a mean of 10% and a standard deviation of 3.6%.

b) Table:

p_i = area under the Standard Normal bell-curve. which i have calculated using excel

Test statistic:

$\chi^2 =\Sigma \frac{(O-E)^2}{E} = 5.296 = \textbf{5.30}$

c) p-value = 0.010 <p-value < 0.025

d) Conclusion:

Do not reject H0; there is not enough evidence to support the claim that the vacancy rates are not normally distributed

e) No, the sample data does not suggest that vacancy rates do not follow the normal distribution.