Amarketing company wants to estimate the proportion of consumers in a certain region of the country who would react favorably to a new marketing campaign. further, the company wants the estimate to have a margin of error of no more than 5 percent with 90 percent confidence. of the following, which is closest to the minimum number of consumers needed to obtain the estimate with the desired precision?

271

Step-by-step explanation:

When the prior estimate of population proportion is not given , then the formula to find the sample size is given by :-

, where E = Margin of error.

z* = Critical z-value.

As per given , we have

E = 5%=0.05

Confidence level = 90%

The critical value of z at 90% is 1.645  (By z-table)

Put all values in the formula , we get

Thus, the minimum sample size needed = 271

Hence , the correct answer is 271 .

To estimate the proportion of consumers in a certain region of the country who would react favorably to a new marketing campaign, we can use formula of sample size.

The minimum size needed is 271.

Given:

The margin of error is.

Confidence level = 90%

Refer the z-table critical value of z at 90% confidence level is .

Calculate the sample size by using following formula.

Substitute the value in above equation.

Thus, the minimum size needed is 271.

Learn more about what  sample size is here:

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step-by-step explanation: