Question

you wish to test the claim that $muleq42$ at a level of significance of $alpha = 0.01$ and are given sample statistics $n = 40$ and $overline{x}=43.8$. assume the population standard deviation is $4.3$. compute the value of the standardized test statistic. round your answer to two decimal places.
a. 1.96
b. 2.65
c. 2.12
d. 3.51

Explanation:

Step1: Recall the formula for the z - test statistic

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

Step2: Substitute the given values into the formula

We are given that \(\bar{x} = 43.8\), \(\mu=42\), \(\sigma = 4.3\), and \(n = 40\)

First, calculate \(\frac{\sigma}{\sqrt{n}}\):
\(\frac{\sigma}{\sqrt{n}}=\frac{4.3}{\sqrt{40}}\approx\frac{4.3}{6.3246}\approx0.68\)

Then, calculate \(z\):
\(z=\frac{43.8 - 42}{0.68}=\frac{1.8}{0.68}\approx2.65\)

Answer:

B. 2.65