poard-Athens Stat xChapter 12 Homework x Oeztamheducation.com/hmtpx Exercise 12-

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poard-Athens Stat xChapter 12 Homework x Oeztamheducation.com/hmtpx Exercise 12-29 Algo Severty ctbes prowided irformation on vacency rates (in percent) in local apartments in the following trequency distribution The sample mean and the sample standard dei ation are 11% and 4 4%, respectively Use Table 3 Vacancy Rate (in percent) quency Less than 6 6 up to 9 9 up to 12 12 or more 10 25 28 a. Choose the appropiate null and altemative hypotheses HO Vacancy rates are normaly dstributed with a mean of 11% and a standard dev, at on of 4 4%. Ha Vacancy rates are not normály distributed with a mean of 11% and a standard deviation of 4 4% Ho vacancy rates are not normally distributed wth a mean of 1 1% and a standard deviation of 4 4% HA Vacancy rates are normaly distributed with a mean of 11% and a standard deviation of 4 4% b. Calculate the value of the test statistic at the 5% signficance 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 statisic c. Approumate the p-value

Explanation / Answer

Exercise 12-29 Algo

Answer: (a) The correct null and alternative hypothesis for example (a) is given as

H0: Vacancy rates are normally distributed with a mean of 11% and a standard deviation of 4.4%.

HA: Vacancy rates are not normally distributed with a mean of 11% and a standard deviation of 4.4%.

(b)

In order to calculate the z-score, we are in need of sample mean , population mean, sample size and sample standard deviation or population standard deviation. we have data as below

Above data is heavely negatively skewed as 76% of the vacancy rates fall in the last two class intervals.

The z-score is 3.80.

(c)

Since z-score is 3.80, therefore p-value is <0.025.

(d)

p-value is <0.025, we reject the H0

There is not enough evidence to support the claim that vacancy rates are normally distributed.

(e)

Yes, sample data support that data is not normally distributed.

Lower Limit Upper Limit Frequency Percentage Cumulative Percentage Less 6 7 10% 10% 6 9 10 14% 24% 9 12 25 36% 60% 12 More 28 40% 100%

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