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 = 0.88, 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 confidence interval becomes wider. This is because a higher confidence level requires capturing the true population parameter with greater certainty, so we need to allow for more possible values.

Step2: Compare the given confidence level \(c = 0.88\) with others

We know that \(0.88<0.90<0.95<0.98\). So the confidence interval for \(c = 0.88\) should be the narrowest among the four intervals (since lower confidence level means less "certainty - seeking" and thus a narrower range of values).

Looking at the intervals:

• Interval A: from \(55.4\) to \(58.8\)
• Interval B: from \(54.5\) to \(59.7\)
• Interval C: from \(55.3\) to \(58.9\)

Calculate the widths:

• Width of A: \(58.8 - 55.4=3.4\)
• Width of B: \(59.7 - 54.5 = 5.2\)
• Width of C: \(58.9 - 55.3=3.6\)

Answer:

A.