Question

for each level of confidence c below, determine the corresponding normal confidence interval. assume each confidence interval is constructed for the same sample statistics. 17. ( c = 0.88 ) 18. ( c = 0.90 ) 19. ( c = 0.95 ) 20. ( c = 0.98 ) 19. for ( c = 0.95 ), choose the corresponding normal confidence interval below. a. b.

Explanation:

Step1: Understand the relationship between confidence level and interval width

As the confidence level \(c\) increases, the width of the confidence interval also increases. This is because a higher confidence level requires capturing a larger proportion of the sampling distribution, so the interval needs to be wider.

Step2: Compare the intervals for different confidence levels

We know that \(0.88<0.90 < 0.95<0.98\). So the confidence interval for \(c = 0.95\) should be wider than the intervals for \(c=0.88\) and \(c = 0.90\), but narrower than the interval for \(c=0.98\).

Looking at the intervals:

• Option A has endpoints \(54.9\) and \(59.3\).
• Option B has endpoints \(55.3\) and \(58.9\).

The interval in Option A is wider than the interval in Option B. Since \(c = 0.95\) is higher than \(c=0.90\) (assuming the other intervals in the original problem for lower confidence levels are narrower) and lower than \(c = 0.98\) (assuming the interval for \(c = 0.98\) is wider), we can match the interval based on width.

Answer:

A.