The image shows a hypothesis testing problem. The main tasks are:

(a) Testing Hypothesis:

• You are asked to test whether $\mu_1 \neq \mu_2$ at the $\alpha = 0.01$ level of significance, assuming both populations are normally distributed.

• The correct hypothesis setup is provided as:

  • Null Hypothesis ($H_0$): $\mu_1 = \mu_2$
  • Alternative Hypothesis ($H_1$): $\mu_1 \neq \mu_2$

(b) Confidence Interval:

• Construct a 99% confidence interval for $\mu_1 - \mu_2$.

Explanation of Choice A:

• The chosen null hypothesis and alternative hypothesis in option A is correct for a two-tailed test. The test is set up to check if the two population means are not equal ($\mu_1 \neq \mu_2$), which corresponds to a two-tailed test.

Do you need help with calculating the p-value or constructing the confidence interval for part (b)?

5 Related Questions:

1. How do you calculate the test statistic for a two-sample t-test?
2. What is the difference between a one-tailed and a two-tailed hypothesis test?
3. How do you interpret a p-value in the context of hypothesis testing?
4. What are the assumptions behind performing a t-test?
5. How do you calculate a 99% confidence interval for the difference between two means?

Tip:

Always check the assumptions for normality and equal variances before performing t-tests.