A research center claims that at least 24% of adults in a certain country think that their taxes will be audited. In a random sample of 800 adults in that country in a recent year, 21% say they are concerned that their taxes will be audited. At a= 0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. ..... (Round to two decimal places as needed. Use a comma to separate answers as needed.) Identify the rejection region(s). Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.) YA. The rejection region is z< - 1.28

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### Statistical Hypothesis Testing Example

A research center claims that at least 24% of adults in a certain country think their taxes will be audited. In a recent sample of 800 adults from that country, 21% say they are concerned about a tax audit. We are tasked with determining if, at a significance level of \( \alpha = 0.10 \), there is enough evidence to reject the center's claim. This involves completing parts (a) through (e) as outlined below.

#### (a) Identify the Rejection Region(s)
- **Option A:** The rejection region is \( z < -1.28 \).

#### (c) Find the Standardized Test Statistic \( z \)
- **Calculated \( z \):** \( z = -1.99 \)

#### (d) Decision on Null Hypothesis
- **Decision:** Choose whether to "reject" or "fail to reject" the null hypothesis based on the calculated \( z \)-value and the identified rejection region.
- **Interpretation:** Determine if there is enough evidence concerning the center's claim.

*Note: The rejection region \( z < -1.28 \) indicates that we reject the null hypothesis if the test statistic is less than -1.28. Since the calculated \( z \) is -1.99, which falls in the rejection region, there is sufficient evidence to reject the center's claim.*

### Conclusion
This example illustrates the process of hypothesis testing using the standardized test statistic method. It provides insight into how statistical evidence can be used to evaluate claims with a pre-determined level of significance.
Transcribed Image Text:### Statistical Hypothesis Testing Example A research center claims that at least 24% of adults in a certain country think their taxes will be audited. In a recent sample of 800 adults from that country, 21% say they are concerned about a tax audit. We are tasked with determining if, at a significance level of \( \alpha = 0.10 \), there is enough evidence to reject the center's claim. This involves completing parts (a) through (e) as outlined below. #### (a) Identify the Rejection Region(s) - **Option A:** The rejection region is \( z < -1.28 \). #### (c) Find the Standardized Test Statistic \( z \) - **Calculated \( z \):** \( z = -1.99 \) #### (d) Decision on Null Hypothesis - **Decision:** Choose whether to "reject" or "fail to reject" the null hypothesis based on the calculated \( z \)-value and the identified rejection region. - **Interpretation:** Determine if there is enough evidence concerning the center's claim. *Note: The rejection region \( z < -1.28 \) indicates that we reject the null hypothesis if the test statistic is less than -1.28. Since the calculated \( z \) is -1.99, which falls in the rejection region, there is sufficient evidence to reject the center's claim.* ### Conclusion This example illustrates the process of hypothesis testing using the standardized test statistic method. It provides insight into how statistical evidence can be used to evaluate claims with a pre-determined level of significance.
**Educational Website Transcription**

**Statistical Analysis of a Research Claim**

A research center claims that at least 24% of adults in a certain country think that their taxes will be audited. In a random sample of 800 adults in that country in a recent year, 21% say they are concerned that their taxes will be audited. With a significance level (α) = 0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below.

**Instructions:**
Round your answers to two decimal places as needed. Use a comma to separate answers as needed.

---

**Identify the Rejection Region(s):**

Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.)

- **A.** The rejection region is \( z < -1.28 \) (Selected)

- **B.** The rejection region is \( z < \) ____

- **C.** The rejection regions are \( z < \) ____ and \( z > \) ____

- **D.** The rejection region is ____ \( < z < \) ____

---

**Hypothesis Testing Decision:**

Test Statistic: \( z \) = ______ (Round to two decimal places as needed.)

- **Reject** the Null Hypothesis

- **Fail to Reject** the Null Hypothesis

Select or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

There [is/is not] ______ enough evidence to [reject/support] the center’s claim.

---

**User Actions:**
- Help me solve this
- View an example
- Get more help

**Interface Elements:** 
- Final check button
- Temperature display: 47°F

**Notes:**
Users are prompted to calculate and reason through the hypothesis test to determine the validity of the research claim regarding adults’ concerns about tax audits in the specified country.
Transcribed Image Text:**Educational Website Transcription** **Statistical Analysis of a Research Claim** A research center claims that at least 24% of adults in a certain country think that their taxes will be audited. In a random sample of 800 adults in that country in a recent year, 21% say they are concerned that their taxes will be audited. With a significance level (α) = 0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. **Instructions:** Round your answers to two decimal places as needed. Use a comma to separate answers as needed. --- **Identify the Rejection Region(s):** Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.) - **A.** The rejection region is \( z < -1.28 \) (Selected) - **B.** The rejection region is \( z < \) ____ - **C.** The rejection regions are \( z < \) ____ and \( z > \) ____ - **D.** The rejection region is ____ \( < z < \) ____ --- **Hypothesis Testing Decision:** Test Statistic: \( z \) = ______ (Round to two decimal places as needed.) - **Reject** the Null Hypothesis - **Fail to Reject** the Null Hypothesis Select or fail to reject the null hypothesis and interpret the decision in the context of the original claim. There [is/is not] ______ enough evidence to [reject/support] the center’s claim. --- **User Actions:** - Help me solve this - View an example - Get more help **Interface Elements:** - Final check button - Temperature display: 47°F **Notes:** Users are prompted to calculate and reason through the hypothesis test to determine the validity of the research claim regarding adults’ concerns about tax audits in the specified country.
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