Q:

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.

Accepted Solution

A:
Answer: 1.88Step-by-step explanation:The confidence interval for population mean is given by :-[tex]\mu\ \pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]Given : Significance level : [tex]1-0.94=0.06[/tex]Critical value : [tex]z_{\alpha/2}=z_{0.06/2}=z_{0.03}[/tex]By using the standard normal distribution table for z, we find the critical value of [tex]z_{0.03}[/tex] corresponds to the p-value 0.03.[tex]z_{0.03}=1.8807936\approx1.88[/tex]Hence, the z-value that was used in the computation must be 1.88 .