Eighty eight cities provided information on vacancy rates (in percent) in local

Question

Eighty eight 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 40%, respectively Use Table 3 Vacancy Rate (in percent) Frequency Less than6 6 up to 9 9 up to 12 12 or more 14 20 31 23 a. Choose the appropriate null and alternative hypotheses O HO Vacancy rates are normally distributed with a mean of 10% and a standard deviation of 4% HA Vacancy rates are not normally distributed with a mean of 10% and a standard deviation of 4%. HO Vacancy rates are not normally distributed with a mean of 10% and a standard deviation of 4%, HA Vacancy rates are normally distributed with a mean of 10% and a standard deviation of 490 b. Calculate the value of the test statistic at the 1% 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

Explanation / Answer

a) hypothesis: 1 st option is correct

b)applying chi square test of goodness of fit:

chi square test statistic =1.89

c) p value =0.5955

Class Limits observed Normal Normal Expected 2=(O-E)2/E lower Upper Bin frequency(O) probabilty probabilty(p) frequency(E=p*O) - 6 -6 14 P(X<6) 0.1587 13.962 0.000 6 - 9 6-9 20 P(6<X<9) 0.2426 21.352 0.086 9 - 12 9-12 31 P(9<X<12) 0.2902 25.535 1.170 12 - inf 12-inf 23 P(12<X<inf) 0.3085 27.151 0.635 Total 88 1 88 1.89

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