You are interested in constructing a 90% confidence interval for the proportion

Question

You are interested in constructing a 90% confidence interval for the proportion of people who will buy a new cell phone this year. Of the 800 randomly selected people surveyed, 382 will buy a new cell phone this year.

A. With 90% confidence the proportion of all people who will buy a cell phone this year is between ----------- and -------------

B. If many groups of 800 randomly selected people were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of people who will buy a new cell phone this year and about percent will not contain the true population proportion.

Explanation / Answer

A) P = 382/800 = 0.4775

confidence interval = P +/- Z0.95 * sqrt (p * (1 - P ) / n)

= 0.4775 + / - 1.645 * sqrt(0.4775 * 0.5225 / 800)

= 0.4775 +/- 0.0291

= 0.4484, 0.5066

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