Question

A $90\%$confidence interval for the mean μ of a population is computed from a random sample and is found to be$90\pm 30$. Which of the following could be the $95\%$confidence interval based on the same data?

a. $90\pm 21$

b. $90\pm 30$

c. $90\pm 39$

d. $90\pm 70$

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

Short answer

The required correct option is$\left(e\right)$

Step-by-step solution

Given information

Confidence interval $=90\pm 30$

Confidence level$=90\%$

The objective is to find out the 95%confidence interval using the same data

The width of the confidence interval is known to be proportional to the sample size. As a result, the width of the interval would become wider for the sample data at $95\%$confidence level. The sample size must be known in order to compute the confidence interval.

Therefore, the correct option is$\left(e\right)$