Roper ASW conducted a survey to learn about American adults’ attitudes toward money and happiness ($Money,$ October $2003$). Fifty-six percent of the respondents said they balance their checkbook at least once a month.

What is the probability that the sample proportion will be within $\pm .04$ of the population proportion?

Question

Roper ASW conducted a survey to learn about American adults’ attitudes toward money and happiness ( $Money,$ October $2003$ ). Fifty-six percent of the respondents said they balance their checkbook at least once a month.

What is the probability that the sample proportion will be within $\pm .04$ of the population proportion?

What is the probability that the sample proportion will be within $\pm .04$ of the population proportion?

Quizlet Admin · Accepted Answer

Given:

* $n$ = Sample size = 400
* $p$ = Population proportion = 56% = 0.56

In this exercise, we determine the probability $P(|\overline{p}-p|<0.04)$  or equivalently $P(-0.03<\overline{p}-p<0.04)$.

*What is the probability distribution of $\overline{p}$?*