A researcher wishes to estimate with 95% confidence, the proportion of the people who own a home computer. A previous study shows that 40% of the interviewed had a computer at home. The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size necessary?

The minimum sample size necessary is 2305.

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:

For this problem, we have that:

95% confidence level

So , z is the value of Z that has a pvalue of , so .

The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size necessary?

We need a sample size of n.

n is found when M = 0.02. So

Rounding up

The minimum sample size necessary is 2305.

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step-by-step explanation:

they will manufacture 8496 cars