Question

Suppose the number of defects in a sweater from a population of sweaters produced from a textile factory are normally distributed with an unknown population mean and a population standard deviation of 0.06 defects. A random sample of sweaters from the population produces a sample mean of x¯=1.3 defects. What value of z should be used to calculate a confidence interval with a 95% confidence level? z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576

Answer 1

Z = 1.96.

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1-0.95)/(2) = 0.025`

Now, we have to find z in the Ztable as such z has a pvalue of
`1-\alpha`.

So it is z with a pvalue of
`1-0.025 = 0.975`, so
`z = 1.96`

The value of z that should be used is Z = 1.96.