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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.

To test H_0: μ = 20 versus H_1: μ < 20, a simple random sample of size n = 16 is obtained from a population that is known to be normally distributed. If x̄ = 18.4 and s = 4.4, compute the test statistic t.

This problem demonstrates how to compute the test statistic for a one-sample t-test where the null hypothesis is μ = 20, sample size n = 16, sample mean x̄ = 18.4, and sample standard deviation s = 4.4. Suitable for college-level statistics students.

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