14. If, after you obtain a 95% confidence interval you find it to be too wide, w

Question

14. If, after you obtain a 95% confidence interval you find it to be too wide, which of the following steps can you take to reduce the width of the confidence interval? (choose all that apply) i) Construct a 90% confidence interval instead of a 95% one. ii) Re-do the 95% confidence interval using a smaller sample size. iii) Construct a 99% confidence interval instead of a 95% one. iv) Re-do the 95% confidence interval using a larger sample size. (a) (i) and (ii) applies (b) (i) and (iv) applies (c) only (i) applies (d) (ii) and (iv) applies

Explanation / Answer

The confidence interval width increases with the confidence level because the critical test statistic value rises with higher confidence.

The margin of error is inversely proportional to the square root of the sample size. Therefore the confidence interval width decreases with an increase in the sample size.

Therefore to reduce the confidence interval width we could either have a larger sample size or we can decrease the confidence level here.

(i) is correct because 90% is lesser confidence than 95% confidence

(iv) is correct here as a larger sample size decreases the confidence interval width as explained above.

Therefore b) is the correct answer here.

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