A statistician constructed the 95 percent confidence interval (2.3, 3.7) to estimate the slope of a regression model for a set of bivariate data with 24 data values. If the sample size n changes but all other things remain the same, which of the following claims about the confidence interval is true ?

A: The interval becomes narrower if n = 20.
B: The interval width remains the same if n = 20.
C: The interval becomes wider if n = 28.
D: The interval becomes narrower if n = 28.
E: The interval width remains the same if n = 28.

Interval is described as the range in which the values fluctuate. This involves one initial or beginning value while the other is the end value and in between these two, the values range.

Given that,

Confidence interval = 95%(2.3, 3.7)

No. of data values = 24

In this case, the true statement about the effect of alteration in the size of the sample would be the interval becoming more concise/narrow in case n become 28 from 24.

Thus, option D is the correct answer.

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