Question

A 90% confidence interval for the mean M of a population is computed from a random sample and is found to be 9 $\pm$3. Which of the following could be the 95% confidence interval based on the same data?

(a) 9 $\pm$1.96 (b) 9 $\pm$2 (c) 9 $\pm$3 (d) 9 $\pm$4

(e) Without knowing the sample size, any of the above answers could be the 95% confidence interval.

Short answer

confidence interval based on the same data is (d)$9\pm 4$

Step-by-step solution

introduction

we know,

the confidence interval is $95\%$

For calculating the mean population the confidence interval is

confidence interval = points estimate$\pm$margin of error

explanation

confidence interval = points estimate$\pm$margin of error

The width of the confidence interval is addressed by the safety buffer and the width is straightforwardly connected with the degree of confidence.

Here, in the event that $95\%$confidence level is utilized rather than $90\%$, the confidence interval would be more extensive which implies that the margin of error ought to be over $3$. Thus, out of the relative multitude of choices, the confidence interval is $9\pm 4$.