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22 randomly picked people were asked if they rented or owned their own home, 9 said they rented. Obtain a point estimate of the proportion of home owners. Use a 95% level of confidence.

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Answer:

True proportion of homeowners in the population lies between 0.333 and 0.847

Explanation:

If 9 out of 22 randomly picked people said they rented their homes, then the remaining 13 must own their homes. Therefore, the point estimate of the proportion of homeowners is:

Point estimate = Number of homeowners / Total number of people surveyed

Point estimate = 13 / 22

Point estimate = 0.59 (rounded to two decimal places)

To calculate the 95% confidence interval for the true proportion of homeowners, we can use the following formula:

Confidence interval = Point estimate ± (Z-value x Standard error)

where the Z-value corresponds to the desired level of confidence and the standard error is given by:

Standard error = sqrt [ (Point estimate x (1 - Point estimate)) / Sample size]

For a 95% confidence interval, the Z-value is 1.96 (from the standard normal distribution). Using the point estimate obtained earlier, the sample size is 22, and we can calculate the standard error as:

Standard error = sqrt [ (0.59 x 0.41) / 22 ]

Standard error = 0.131 (rounded to three decimal places)

Substituting these values into the formula, we get:

Confidence interval = 0.59 ± (1.96 x 0.131)

Confidence interval = 0.59 ± 0.257

Confidence interval = (0.333, 0.847)

Therefore, with 95% confidence, we can say that the true proportion of homeowners in the population lies between 0.333 and 0.847.

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