Question

for each level of confidence c below, determine the corresponding normal confidence interval. assume each confic 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 $c = 0.98$, choose the corresponding normal confidence interval below.

○ a.
○ b.
○ c.

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 widths of the given intervals

• Interval in option A: From \(54.5\) to \(59.7\). The width is \(59.7 - 54.5=5.2\)
• Interval in option B: From \(55.4\) to \(58.8\). The width is \(58.8 - 55.4 = 3.4\)
• Interval in option C: From \(54.9\) to \(59.3\). The width is \(59.3 - 54.9=4.4\)

Since \(c = 0.98\) is the highest confidence level among \(c=0.88\), \(c = 0.90\), \(c=0.95\) and \(c=0.98\), the corresponding confidence interval should be the widest.

Answer:

A.