Question

Suppose the number of free throws in a basketball game by one player are normally distributed with a standard deviation 0.97 free throws. A random sample of basketball players from the population produces a sample mean of x¯=4.9 free throws. What value of z should be used to calculate a confidence interval with a 95% confidence level? 20.10 1.282 20.05 1.645 0.025 1.960 20.005 2.576 2.326

Answer 1

Answer: 1.960

Explanation:

The value of z we use to calculate a confidence interval with a (
`1-\alpha`) confidence level is a two-tailed test value i.e. represented by :-

`z_(\alpha/2)`

Given : The level of confidence:
`1-\alpha=0.95`

Then, significance level :
`\alpha: 1-0.95=0.05`

With the help of standard normal distribution table for z , we have

`z_(\alpha/2)=z_(0.05/2)=z_(0.025)=1.960`

Hence, the value of z should be used to calculate a confidence interval with a 95% confidence level =1.960