Question

suppose you want to test the claim that μ≠3.5. given a sample size of n = 35 and a level of significance of α = 0.05, when should you reject h₀?

a. reject h₀ if the standardized test statistic is greater than 2.33 or less than - 2.33
b. reject h₀ if the standardized test statistic is greater than 1.645 or less than - 1.645.
c. reject h₀ if the standardized test statistic is greater than 1.96 or less than - 1.96.
d. reject h₀ if the standardized test statistic is greater than 2.575 or less than - 2.575

Explanation:

Step1: Determine the type of test

The claim is \(\mu
eq3.5\), so this is a two - tailed test.

Step2: Find the critical values

For a two - tailed test with \(\alpha = 0.05\), the area in each tail is \(\frac{\alpha}{2}=\frac{0.05}{2}=0.025\).
Looking up in the standard normal distribution table (z - table), the z - score corresponding to an area of \(1 - 0.025=0.975\) is \(z = 1.96\), and the z - score corresponding to an area of \(0.025\) is \(z=- 1.96\).

Answer:

C. Reject \(H_0\) if the standardized test statistic is greater than \(1.96\) or less than \(-1.96\)