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Answer:
Sample size of 586 or higher.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error is:
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
What sample size could be 95% confident that the estimated (sample) proportion is within 4 percentage points of the true population proportion?
Sample size of at least n when
42.1% of women-owned businesses provided retirement plans contributions, which means that . So
We need a sample size of 586 or higher.