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This image shows a hypothesis testing problem related to job satisfaction. Let's break down the steps outlined in the problem and how to solve it.

### Problem Overview:
- A researcher claims that the percentage of workers satisfied with their jobs has decreased from the previously known 22%.
- A sample of 100 adults is surveyed.
- The test is conducted at a significance level of \( \alpha = 0.05 \).

### Preliminary Questions:

**a.** Is it safe to assume that \( n < 0.05 \) of all subjects in the population?
- The answer marked is **Yes**. This means the sample size (100) is likely less than 5% of the population of all workers, satisfying one condition for performing hypothesis testing.

**b.** Verify \( np(1 - p) \geq 10 \). The calculation shows:
\[
np(1 - p) = 17.2
\]
- This meets the condition \( np(1 - p) \geq 10 \), allowing the normal approximation to the binomial distribution.

### Test the Claim:

**a.** Express the null and alternative hypotheses:
- \( H_0: p = 0.22 \) (the population proportion is still 22%)
- \( H_a: p < 0.22 \) (the researcher claims it has decreased)

**b.** The researcher surveyed 100 adults, and 55 indicated they were satisfied. The test statistic \( z \) is calculated:
\[
z = 7.96
\]
This is an unusually large \( z \)-score, indicating strong evidence against the null hypothesis.

**c.** The next step asks for the p-value, which is to be rounded to 4 decimal places. Based on the \( z \)-value of 7.96, the p-value will be very small, but we can use statistical software or a z-table to find it accurately.

### Summary of Approach:

1. **Hypotheses**:
   - \( H_0: p = 0.22 \)
   - \( H_a: p < 0.22 \)
2. **Test Statistic**: The given \( z \)-value is 7.96.
3. **p-value**: We would compute the p-value from the normal distribution using this \( z \)-value. For such a high \( z \), the p-value will be extremely close to zero.

Would you like me to compute the exact p-value or clarify any other part of the process?

---

Here are 5 related questions:
1. What does a very small p-value indicate in hypothesis testing?
2. How is the test statistic \( z \)-value calculated for proportions?
3. What assumptions are necessary for using the normal approximation in proportion hypothesis testing?
4. How would the hypothesis test change if the claim was that the percentage has increased?
5. How would you interpret the results if the p-value was slightly higher than the significance level?

**Tip**: Always verify conditions such as sample size and independence when using the normal approximation for proportions.

A researcher claims that the percentage of workers satisfied with their jobs has decreased from the previously known 22%. A sample of 100 adults is surveyed. The test is conducted at a significance level of α = 0.05.

Test a researcher's claim that job satisfaction has decreased from 22%. The problem involves hypothesis testing for proportions, using the z-test and verifying normal approximation conditions.

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