18. In a random sample (N-105) drawn from the wealthiest neighborhoods in a comm

Question

18. In a random sample (N-105) drawn from the wealthiest neighborhoods in a community, 73% of the respondents indicated that they had voted for the Republican candidate in the last presidential election in the community as a whole, 61% had voted for the Republican candidate, were those in the wealthiest neighborhoods significantly more likely to have voted Republican than the community as a whole:? Perform a hypothesis test to answer that question. Set alpha at .05. (Explain your reasons for selecting the test you use.)

Explanation / Answer

Solution:

Here, we have to use the z test for population proportion.

The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The proportion of wealthiest neighborhoods in a community who voted for republican is 61%.

Alternative hypothesis: Ha: The proportion of wealthiest neighborhoods in a community who voted for republican is more than 61%.

H0: p = 0.61 versus Ha: p > 0.61

We are given

Sample Proportion = P = 0.73

Test statistic = Z = (P – p)/sqrt(pq/n)

Where, q = 1 – p = 1 – 0.61 = 0.39,

Sample size = n = 105

= 0.05

Z = (0.73 – 0.61) / sqrt(0.61*0.39/105)

Z = 0.12/ 0.0476

Z = 2.521034

P-value = 0.0059 (by using z-table or excel)

P-value < = 0.05

So, we reject the null hypothesis that the proportion of wealthiest neighborhoods in a community who voted for republican is 61%.

There is sufficient evidence to conclude that the proportion of wealthiest neighborhoods in a community who voted for republican is more than 61%.

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