The image describes a hypothesis testing scenario, where you are tasked with testing:

$H_0: \mu = 20 \quad \text{versus} \quad H_1: \mu < 20$

A random sample of size $n = 16$ is obtained from a population that is known to be normally distributed. Part (a) asks to compute the test statistic $t$, given:

• Sample mean $\bar{x} = 18.4$
• Sample standard deviation $s = 4.4$
• Population mean under the null hypothesis $\mu_0 = 20$

The formula for the $t$-statistic in a one-sample t-test is:

$t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$

Now let's calculate:

$t = \frac{18.4 - 20}{4.4 / \sqrt{16}} = \frac{-1.6}{4.4 / 4} = \frac{-1.6}{1.1} \approx -1.45$

Thus, the test statistic $t \approx -1.45$ (rounded to two decimal places).

Would you like help with parts (b)-(d) or further clarification?

Here are 5 related questions that could help your understanding:

1. What is the critical value for this one-tailed test at a specific significance level (e.g., 0.05)?
2. How do you interpret the results of the hypothesis test based on the test statistic?
3. What is the p-value for this test statistic, and how does it relate to the conclusion?
4. Can you describe the steps to check assumptions for using the t-test in this scenario?
5. How would the test change if it were a two-tailed hypothesis test?

Tip: Always check whether you're performing a one-tailed or two-tailed test, as it changes how you compare the test statistic to the critical value or p-value.