Question

A random sample of size 100 was taken from a population. A 94% confidence interval to estimate the mean of the population was computed based on the sample data. The confidence interval for the mean is: (107.62,129.75). What is the z-value that was used in the computation. Round your z-value to 2 decimal places.

Answer 1

Answer: 1.88

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\mu\ \pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Significance level : $1-0.94=0.06$

Critical value : $z_{\alpha/2}=z_{0.06/2}=z_{0.03}$

By using the standard normal distribution table for z, we find the critical value of $z_{0.03}$ corresponds to the p-value 0.03.

$z_{0.03}=1.8807936\approx1.88$

Hence, the z-value that was used in the computation must be 1.88 .