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.

1. ( c = 0.88 ) 18. ( c = 0.90 ) 19. ( c = 0.95 ) 20. ( c = 0.98 )
2. for ( c = 0.90 ), choose the corresponding normal confidence interval below.

○ a.
○ b.
○ c.

Explanation:

Step1: Understand the relationship between confidence level and confidence interval width

As the confidence level \(c\) increases, the width of the confidence interval increases. This is because a higher confidence level requires capturing a larger proportion of the sampling distribution, so the interval must be wider. Conversely, a lower confidence level results in a narrower interval.

Step2: Compare the confidence intervals for different \(c\) values

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

• Option A has a wider interval (likely for a higher \(c\) like \(0.95\) or \(0.98\))
• Option B has a narrower interval (likely for a lower \(c\) like \(0.88\))
• Option C has an intermediate - width interval which is appropriate for \(c = 0.90\)

Answer:

C.