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A survey was run by a high school student in order to determine what proportion of mortgage-holders in his town expect to own

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Answer #1

a) Answer :

The sample size is n = 41.

The proportion of mortgage holders that did expect to own their house within 10 years is p = 0.61

Z-value for 95% confidence interval is Z = 1.96

The margin of error is calculated by

Margin of error = Z * \sqrt{(p * (1-p))/n}

                         = 1.96 * \sqrt{(0.61 * (1-0.61))/41}

                         = 1.96 * 0.076

                         = 0.15

Therefore, the margin of error is 0.15

b) Answer :

The sample size is n = 82.

The proportion of mortgage holders that did expect to own their house within 10 years is p = 0.61

Z-value for 95% confidence interval is Z = 1.96

The margin of error is calculated by

Margin of error = Z * \sqrt{(p * (1-p))/n}

                         = 1.96 * \sqrt{(0.61 * (1-0.61))/82}

                         = 1.96 * 0.054

                         = 0.11

Therefore, the margin of error is 0.11

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