Answer :
Sure! Let's go through the process of determining the correct null and alternate hypotheses for this scenario.
1. Understanding Hypotheses:
- The null hypothesis (H₀) is a statement that there is no effect, no difference, or no change. It represents the status quo or the standard used for comparison.
- The alternate hypothesis (Hₐ) is what we want to test for. It's the statement that indicates there is an effect, a difference, or a change from the status quo.
2. What We Know:
- The mean price of a prom dress for the general population of high school students (8,000 students) is [tex]$195.00.
- Alyssa believes that students at her school spent more on prom dresses, specifically that they spent more than $[/tex]195.00.
3. Formulating Hypotheses:
- The null hypothesis should reflect that there is no difference from what is generally known. Therefore, the null hypothesis (H₀) would be that the mean price is [tex]$195.00.
- H₀: μ = 195
- Alyssa's belief leads to the alternate hypothesis that the mean price is greater than $[/tex]195.00. She believes students spend more.
- Hₐ: μ > 195
4. Conclusion:
- The correct set of hypotheses for Alyssa’s investigation is:
- Null Hypothesis (H₀): μ = 195
- Alternate Hypothesis (Hₐ): μ > 195
This setup allows Alyssa to statistically test if the average amount spent on prom dresses in her school is greater than $195.00, supporting her claim that her school is more fashion conscious.
1. Understanding Hypotheses:
- The null hypothesis (H₀) is a statement that there is no effect, no difference, or no change. It represents the status quo or the standard used for comparison.
- The alternate hypothesis (Hₐ) is what we want to test for. It's the statement that indicates there is an effect, a difference, or a change from the status quo.
2. What We Know:
- The mean price of a prom dress for the general population of high school students (8,000 students) is [tex]$195.00.
- Alyssa believes that students at her school spent more on prom dresses, specifically that they spent more than $[/tex]195.00.
3. Formulating Hypotheses:
- The null hypothesis should reflect that there is no difference from what is generally known. Therefore, the null hypothesis (H₀) would be that the mean price is [tex]$195.00.
- H₀: μ = 195
- Alyssa's belief leads to the alternate hypothesis that the mean price is greater than $[/tex]195.00. She believes students spend more.
- Hₐ: μ > 195
4. Conclusion:
- The correct set of hypotheses for Alyssa’s investigation is:
- Null Hypothesis (H₀): μ = 195
- Alternate Hypothesis (Hₐ): μ > 195
This setup allows Alyssa to statistically test if the average amount spent on prom dresses in her school is greater than $195.00, supporting her claim that her school is more fashion conscious.
