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An ice cream truck driver randomly sampled people that purchased ice cream on a Friday night. He...

Question:

An ice cream truck driver randomly sampled people that purchased ice cream on a Friday night. He wanted to find out how many people preferred chocolate ice cream over vanilla ice cream. The proportion of customers that preferred chocolate ice cream was 0.56, with a margin of error of 0.12.

Construct a confidence interval for the proportion of customers that preferred chocolate ice cream.

Confidence interval

There are two types of estimation for population parameters, which include the point estimation and interval estimation. The confidence interval includes the lower and upper limits, where the lower limit for the population proportion is the difference between the sample proportion and margin of error.

Answer and Explanation:

Given Information

Margin of error; 0.12

Proportion value; 0.56


The confidence interval for the proportion of customers that preferred chocolate ice cream is calculated as follows;

{eq}\begin{align*} P\left( {\hat p - E < p < \hat p + E} \right) &= 1 - \alpha \\ P\left( {0.56 - 0.12 < p < 0.56 + 0.12} \right) &= 1 - \alpha \\ P\left( {0.44 < p < 0.68} \right) &= 1 - \alpha \end{align*} {/eq}

Therefore, the confidence interval is (0.44, 0.68).


Learn more about this topic:

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Finding Confidence Intervals with the Normal Distribution

from Statistics 101: Principles of Statistics

Chapter 9 / Lesson 3
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