In hypothesis testing, the decision to reject or fail to reject the null hypothesis depends on the comparison between the test statistic $t$ and the critical value $t_0$. Here's how to interpret the given situation:

You are given the critical value $t_0 = 1.829$, and you need to evaluate if the test statistic is greater or less than this value.

For part (a) $t = 1.896$:

• The test statistic $t = 1.896$ is greater than the critical value $t_0 = 1.829$.
• This means the test statistic falls to the right of the critical value, which implies the observed result is significant.

Conclusion: Since $t = 1.896 > 1.829$, you should reject the null hypothesis.

Thus, the correct answer is:

B. Reject $H_0$, because $t > 1.829$.

Would you like to see an explanation for the other parts or any further clarification on hypothesis testing? Here's a set of related questions for deeper understanding:

1. What is the interpretation of failing to reject the null hypothesis?
2. How do you determine the critical value $t_0$ in hypothesis testing?
3. How does a two-tailed test differ from a one-tailed test in hypothesis testing?
4. What happens if the test statistic is exactly equal to the critical value $t_0$?
5. How do you choose the significance level $\alpha$ in hypothesis testing?

Tip: Always double-check the direction of the inequality when comparing the test statistic to the critical value to make the correct decision.