Question

A grocery store chain has been tracking data on the number of shoppers that use coupons. the data shows that 71% of all shoppers use coupons. 36 times out of 40 these results were considered accurate to within 2.5%. what is the confidence interval?

Answer 1

The confidence interval comes out to be (0.685,0.735).

Calculating the Confidence Level and Other Terms

The confidence level can be calculated as follows,

z = $\frac{36}{40} * 100%$%  

z = 90 %

The margin error is given as, E= 0.025

The p value in this case is 0.71

Calculating the Confidence Interval

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.

Confidence interval can be obtained by using the following formula,

(p-E, p+E) = (0.71-0.025, 0.71+0.025).

Therefore, the confidence interval is (0.685, 0.735).

Learn more about confidence interval here:

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