Question

you wish to test the claim that \\( \mu = 780 \\) at a level of significance of \\( \alpha = 0.01 \\) and are given sample statistics \\( n = 35 \\), \\( \overline { x } = 750 \\). assume the population standard deviation is 82. compute the value of the standardized test statistic. round your answer to two decimal places.
oa. -3.82
ob. -5.18
oc. -4.67
od. -2.16

Explanation:

Step1: Recall the formula for the z - test statistic

The formula for the z - test statistic is \(z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\)

Step2: Substitute the given values into the formula

We are given \(\bar{x} = 750\), \(\mu=780\), \(\sigma = 82\), and \(n = 35\)

First, calculate the denominator \(\frac{\sigma}{\sqrt{n}}=\frac{82}{\sqrt{35}}\approx\frac{82}{5.916}\approx13.86\)

Then, calculate the numerator \(\bar{x}-\mu=750 - 780=- 30\)

Now, find \(z=\frac{-30}{13.86}\approx - 2.16\)

Answer:

D. - 2.16