Question

(a) construct a (90%) confidence interval for the population mean (mu). enter the values for the lower and upper limits and the mean to graph.

part 2 of 2
(b) if the sample size were (n = 46), would the confidence interval be narrower or wider?
the confidence interval would be select

Explanation:

Identify the given parameters

Using the Confidence Interval and Margin of Error knowledge points

$$
LATEXBLOCK0
$$

Analyze the effect of sample size on margin of error

Using the Margin of Error knowledge point

$$
LATEXBLOCK1
$$

Determine the change in interval width

Since the new sample size \(n = 46\) is larger than the original sample size (implied by the context of constructing a narrower/wider interval from a smaller initial sample size, as increasing \(n\) increases the denominator \(\sqrt{n}\)):

$$
LATEXBLOCK2
$$

A smaller margin of error \(E\) results in a narrower confidence interval.

Answer:

narrower