A 95% confidence interval for the mean price of textbooks at UCLA in the spring

Question

A 95% confidence interval for the mean price of textbooks at UCLA in the spring quarter of 2010, based on a random sample taken by statistician David Diez. was ($58.30,$86.14). Assuming that nothing else changed, what would have been the effect of on the confidence interval if the sample size had been smaller? Assume that the necessary conditions for finding the confidence interval hold, and pick the best answer. (a) The confidence interval would have been wider. (b) The confidence interval would have been narrower. (c) The confidence level would have been higher. (d) The confidence level would have been lower. (e) Answers a and c are both correct. (f) Answers b and d are both correct.

Explanation / Answer

If we have a smaller sample size, the standard error will be bigger, so the margin of error will be bigger.

Hence, the confidence interval will be wider.

Hence,

OPTION A. [ONLY 1 ANSWER]

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