Question

suppose you want to test the claim that $mu = 3.5$. given a sample size of $n = 46$ and a level of significance of $alpha = 0.1$, when should you reject $h_0$?

a. reject $h_0$ if the standardized test statistic is greater than $1.645$ or less than $-1.645$.
b. reject $h_0$ if the standardized test statistic is greater than $1.96$ or less than $-1.96$
c. reject $h_0$ if the standardized test statistic is greater than $2.575$ or less than $-2.575$
d. reject $h_0$ if the standardized test statistic is greater than $2.33$ or less than $-2.33$.

Explanation:

Step1: Determine the type of test

Since the claim is \(\mu = 3.5\), this is a two - tailed test.

Step2: Find the critical value

For a two - tailed test with \(\alpha=0.1\), the significance level in each tail is \(\frac{\alpha}{2}=\frac{0.1}{2} = 0.05\).
Looking up the \(z\) - value in the standard normal distribution table, the \(z\) - value corresponding to an area of \(1 - 0.05=0.95\) is \(z = 1.645\).
So, the rejection region is \(z>1.645\) or \(z < - 1.645\).

Answer:

A. Reject \(H_0\) if the standardized test statistic is greater than \(1.645\) or less than \(-1.645\).