Question

After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation? Group of answer choices Increase the sample size. Reduce the population variance. Increase the level of confidence for the interval. Decrease the sample size.

Answer 1

The best recommendation is to: Increase the sample size.

Explanation:

The width of a confidence interval
`W=2* CV* (SD)/(√(n))` ,depends on three things,

1. Sample size (n)
2. Standard deviation
3. Confidence level

To decrease the width the following options can be used:

• Increase the sample size.

Since the sample is inversely proportional to the width of the confidence interval, increasing the value of n will decrease the width.

• Decrease the standard deviation.

The standard deviation is directly proportional to the width of the confidence interval. On decreasing the standard deviation value the width of the interval will also decrease.

• Decrease the confidence level.

The critical value of the distribution is based on the confidence level. Higher the confidence level, higher will be critical value.

So, on deceasing the confidence level the critical value will decrease, hence decreasing the width of the interval.

Thus, the best recommendation is to: Increase the sample size.