Question

Let us use confidence intervals to compare people who own or are buying a home among those that are married versus those who pay rent among those that are married.

1. Calculate pˆ for the group of homeowners that are married.

2. For a confidence level of ell = .97, determine the z-score for which 97% of normally

   distributed data falls within z deviations of the mean.

3. Calculate pˆ for the group of renters that are married.

4. Now compare these two intervals. Do the intervals overlap or not? What association do we have or not have between marriage and homeownership due to whether or not the intervals overlap?

	Married	Never Married	Total
Owns or is Buying	9,178	1,785	10,963
Pays Rent	1,867	2,282	4,149
Total	11,045	4,067	15,112

Answer 1

Let the population proportion of houseowners that are married be denoted by p₁. The sample proportion of house owners that are married is given by

The sample size (n₁) is 10963

The 97% confidence interval for p₁ is given by

Let the population proportion of renters that are married be denoted by p₂. The sample proportion of house owners that are married is given by

The sample size (n₂) is 4149

The 97% confidence interval for p₁ is given by

The confidence interval of the sample proportion of married renters is much lower than that for the sample proportion of married house owners. So it can be concluded that the population proportion of married renters is much less than the population proportion of the married house owners at 3% level of significance.

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