Setting up the Hypothesis Test and interpret the meaning of it it\'s required. A

Question

Setting up the Hypothesis Test and interpret the meaning of it it's required. Also, compare the p-value with alpha and reject or do not reject Ho for each exercise.
15. Sports Facilities. A researcher investigated whether there has been a suburban-to-urban shift in the location of major sport facilities. In 1985. 40% of all major sport facilities were located downtown, 30% in central city, and 30% in suburban areas. The new study showed that, of all the major sports franchises, 58 were downtown, 26 in a central city, and 29 in a suburban area. Test whether the population proportions have changed. using level of significance a 0.05

Explanation / Answer

Solution:

Here, we have to use the z test for the two population proportions. The null and alternative hypothesis for this test is given as below:

H0: p1 = p2 versus Ha: p1 > p2

We are given level of significance or alpha value = 0.05

The test statistic formula is given as below:

Z = (P1 – P2) / sqrt[(P1Q1/N1)+(P2Q2/N2)]

We have, P1 = 0.40, P2 = 0.30, Q1 = 1 – 0.40 = 0.60, Q2 = 1 – 0.30 = 0.70, N1 = 58, N2 = 26

Z = (0.40 – 0.30) / sqrt[(0.40*0.60/58)+(0.30*0.70/26)]

Z = 0.904807

P-value = 0.817216

Alpha value = 0.05

P-value > Alpha value

So, we do not reject the null hypothesis that there is no any significant suburban to urban shift in the location major sport facilities.

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