Question

suppose you want to test the claim that μ < 65.4. given a sample size of n = 35 and a level when should you reject h₀?
a. reject h₀ if the standardized test statistic is less than -2.33.
b. reject h₀ if the standardized test is less than -1.645.
c. reject h₀ if the standardized test statistic is less than -1.96.
d. reject h₀ if the standardized test statistic is less than -1.28.

Explanation:

Step1: Determine the type of test

The claim is \(\mu < 65.4\), so it is a left - tailed test.

Step2: Recall the significance level

Since the level of significance is not given in the problem, but in common - sense hypothesis testing problems (if not specified, we assume \(\alpha=0.05\) for a one - tailed test).
For a left - tailed test with \(\alpha = 0.05\), the critical value \(z\) is obtained from the standard normal distribution table.
The critical value \(z\) for a left - tailed test with \(\alpha=0.05\) is \(z=- 1.645\). We reject the null hypothesis \(H_0\) when the standardized test statistic \(z\) is less than the critical value.

Answer:

B. Reject \(H_0\) if the standardized test is less than \(-1.645\).