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Answer :
To address Alyssa's belief that her school is more fashion-conscious, we need to set up and identify the correct null and alternate hypotheses based on statistical testing principles. Let's go through the process step-by-step:
1. Understand the Problem: Alyssa believes students at her school spend more on prom dresses than what was found in the survey of 8,000 students, where the average price was \[tex]$195.
2. Define the Parameters:
- Population Mean (\(\mu\)): The true average price spent on a prom dress in Alyssa's school.
3. Setting Up Hypotheses:
- Null Hypothesis (\(H_0\)): The null hypothesis is a statement of no effect or no difference, and in this scenario, it suggests that the mean expenditure in Alyssa's school is \$[/tex]195. This baseline value is based on the overall mean from the survey.
- [tex]\(H_0: \mu = 195\)[/tex]
- Alternate Hypothesis ([tex]\(H_a\)[/tex]): The alternate hypothesis reflects Alyssa's belief that students at her school spend more than the average of \[tex]$195. Thus, it is a one-sided hypothesis indicating that the mean is greater than \$[/tex]195.
- [tex]\(H_a: \mu > 195\)[/tex]
4. Identify the Correct Pair: We now match the hypotheses to the options provided:
- [tex]\(H_0: \mu = 195; H_a: \mu > 195\)[/tex]
Given these hypotheses, we have identified the correct null and alternate hypotheses that align with Alyssa's suspicion and the statistical principles involved.
1. Understand the Problem: Alyssa believes students at her school spend more on prom dresses than what was found in the survey of 8,000 students, where the average price was \[tex]$195.
2. Define the Parameters:
- Population Mean (\(\mu\)): The true average price spent on a prom dress in Alyssa's school.
3. Setting Up Hypotheses:
- Null Hypothesis (\(H_0\)): The null hypothesis is a statement of no effect or no difference, and in this scenario, it suggests that the mean expenditure in Alyssa's school is \$[/tex]195. This baseline value is based on the overall mean from the survey.
- [tex]\(H_0: \mu = 195\)[/tex]
- Alternate Hypothesis ([tex]\(H_a\)[/tex]): The alternate hypothesis reflects Alyssa's belief that students at her school spend more than the average of \[tex]$195. Thus, it is a one-sided hypothesis indicating that the mean is greater than \$[/tex]195.
- [tex]\(H_a: \mu > 195\)[/tex]
4. Identify the Correct Pair: We now match the hypotheses to the options provided:
- [tex]\(H_0: \mu = 195; H_a: \mu > 195\)[/tex]
Given these hypotheses, we have identified the correct null and alternate hypotheses that align with Alyssa's suspicion and the statistical principles involved.
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