Question

researchers survey 1000 grocery store customers and find that, when given a choice, 68% of these customers prefer using the self - checkout. when a 95% confidence interval is constructed based on this sample of data, the interval is from 0.651 to 0.709. given what you know and understand about confidence intervals, which one of the following statements is most accurate?
with 95% confidence, approximately 68% of the sample prefer using the self - checkout option.
between 65.1% and 70.9% of all possible samples will produce sample proportions in this range.
between 65.1% and 70.9% of all grocery store customers prefer using the self - checkout.
if the sample size were increased, this would make the interval narrower, but only if the confidence level is also lowered.
none of the above answer options are correct.

Explanation:

• The first option is incorrect because 68% is the sample proportion, and confidence intervals are about the population parameter, not the sample proportion in this context.
• The second option is wrong. A confidence interval is not about the proportion of samples that produce sample - proportions in the range. It is about the population parameter.
• The third option is incorrect. A confidence interval gives a range of values within which we are confident the population proportion lies, not that a certain proportion of the population is within that range.
• The fourth option is wrong. Increasing the sample size will make the interval narrower regardless of the confidence level (a higher confidence level will widen the interval, but increasing \(n\) has its own independent effect of narrowing the interval).

Answer:

None of the above answer options are correct.