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

Step-by-step 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