Question

Question was provided via image upload.

Explanation:

Identify the context

The question asks for the correct alternative hypothesis.
The image shows "Part 2 of 3".
The options involve a parameter value of 20.

Analyze the options

Using the Hypothesis Testing knowledge point:
An alternative hypothesis \(H_1\) (or \(H_a\)) represents the claim being tested.
It must contain an inequality: \(
e\), \(<\), or \(>\).
Thus, \(H_1: p = 20\) is incorrect because it uses an equality.

Determine the parameter

Hypotheses test population parameters like \(\mu\) (mean), \(p\) (proportion), or \(\sigma\) (standard deviation).
The options present \(\mu\), \(p\), and \(\sigma\).
Without Part 1, we look at the selected option in the image.
The first option \(H_1: \mu < 20\) is marked with a selected/correct indicator.

Formulate the conclusion

The selected correct alternative hypothesis is \(H_1: \mu < 20\).
This represents a left-tailed test for a population mean.

Answer:

• (A) \(H_1 : \mu < 20\) (Correct answer)
• (B) \(H_1 : \mu > 20\)
• (C) \(H_1 : p = 20\)
• (D) \(H_1 : \sigma < 20\)