A group of gemologists are interested in studying the average money spent on an engagement ring. In 2020, the average money spent was $6,100. Because of COVID-19, the gemologists think the average has increased for 2021. If the gemologists carry out a hypothesis test, what value forms the rejection region? Select the single best answer choice. O alternative hypothesis critical value null hypothesis

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### Hypothesis Testing and The Rejection Region

**Introduction:**
A group of gemologists is interested in studying the average money spent on an engagement ring. In 2020, the average amount spent was $6,100. Due to the effects of COVID-19, the gemologists hypothesize that the average spending has increased in 2021. They decide to carry out a hypothesis test to explore this assumption.

**Question:**
If the gemologists carry out a hypothesis test, what value forms the rejection region? Select the single best answer choice from the options below:

1. Alternative Hypothesis
2. Critical Value
3. Null Hypothesis

*Choose the correct answer to understand the hypothesis testing process better and learn about the concept of the rejection region.*

### Explanation:
- **Null Hypothesis (H0):** A statement that there is no effect or no difference, and it represents the status quo. In this case, the null hypothesis might be that the average money spent in 2021 is still $6,100.
  
- **Alternative Hypothesis (H1):** A statement that contradicts the null hypothesis. It suggests there is an effect or a difference. Here, the alternative hypothesis would be that the average amount spent in 2021 has increased compared to 2020.
  
- **Critical Value:** A threshold value that defines the boundary for rejecting the null hypothesis. It is determined based on the significance level (α) chosen for the test (commonly 0.05). This value forms the "rejection region."

**Answer:**
The **critical value** forms the rejection region. If the test statistic falls into this region, the null hypothesis is rejected in favor of the alternative hypothesis.

Understanding these concepts is crucial for interpreting the results of hypothesis tests and making informed conclusions based on statistical evidence.
Transcribed Image Text:### Hypothesis Testing and The Rejection Region **Introduction:** A group of gemologists is interested in studying the average money spent on an engagement ring. In 2020, the average amount spent was $6,100. Due to the effects of COVID-19, the gemologists hypothesize that the average spending has increased in 2021. They decide to carry out a hypothesis test to explore this assumption. **Question:** If the gemologists carry out a hypothesis test, what value forms the rejection region? Select the single best answer choice from the options below: 1. Alternative Hypothesis 2. Critical Value 3. Null Hypothesis *Choose the correct answer to understand the hypothesis testing process better and learn about the concept of the rejection region.* ### Explanation: - **Null Hypothesis (H0):** A statement that there is no effect or no difference, and it represents the status quo. In this case, the null hypothesis might be that the average money spent in 2021 is still $6,100. - **Alternative Hypothesis (H1):** A statement that contradicts the null hypothesis. It suggests there is an effect or a difference. Here, the alternative hypothesis would be that the average amount spent in 2021 has increased compared to 2020. - **Critical Value:** A threshold value that defines the boundary for rejecting the null hypothesis. It is determined based on the significance level (α) chosen for the test (commonly 0.05). This value forms the "rejection region." **Answer:** The **critical value** forms the rejection region. If the test statistic falls into this region, the null hypothesis is rejected in favor of the alternative hypothesis. Understanding these concepts is crucial for interpreting the results of hypothesis tests and making informed conclusions based on statistical evidence.
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