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A survey was given to a random sample of 100 people in a small city.  A survey...

A survey was given to a random sample of 100 people in a small city.  A survey was also given to a random sample of 100 people in a large city.  In the survey, everyone was asked if they felt not safe, somewhat safe or very safe in their homes. A p-value for a chi-square test was calculated to be 0.12. Which of the following is the most appropriate conclusion at the 1% significance?

a.   Living in the larger city does not make people feel significantly less safe in their homes than living in the smaller city.

b.   The distribution of the population proportions for feeling not safe, somewhat safe or very safe in their homes is significantly different for the small and large city.

c.   The distribution of the population proportions for feeling not safe, somewhat safe or very safe in their homes is the same for the small and large city.

d.   The distribution of the population proportions for feeling not safe, somewhat safe or very safe in their homes is not significantly different between the small and large city.

Math   Statistics-And-Probability   
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Answer #1

Null Hypothesis: The distribution of the population proportions for feeling not safe, somewhat safe or very safe in their homes is the same for the small and large city.

Alternative Hypothesis: The distribution of the population proportions for feeling not safe, somewhat safe or very safe in their homes is significantly different for the small and large city.

Given, p-value =

Level of significance =

Since p-value > we fail to reject the null hypothesis.

Hence, the distribution of the population proportions for feeling not safe, somewhat safe or very safe in their homes is NOT significantly different for the small and large city.

Therefore, Option-D is the correct answer.

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