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Answer :
To solve this problem, let's determine the correct null hypothesis ([tex]\(H_0\)[/tex]) and alternate hypothesis ([tex]\(H_a\)[/tex]) based on the scenario described.
1. Understanding the Hypotheses:
- Null Hypothesis ([tex]\(H_0\)[/tex]): This hypothesis represents the status quo or a baseline that Alyssa wants to test against. In this case, it is the claim that the mean price of a prom dress in her school is equal to the population mean, which is [tex]$19,500.
- Alternate Hypothesis (\(H_a\)): This hypothesis represents Alyssa's belief or what she thinks could be true. Alyssa believes that her school's students spend more on prom dresses than the average. Therefore, the alternate hypothesis would be that the mean price of a prom dress in her school is greater than $[/tex]19,500.
2. Formulating the Hypotheses:
- The Null Hypothesis ([tex]\(H_0\)[/tex]) would be: [tex]\(\mu = 19500\)[/tex].
- The Alternate Hypothesis ([tex]\(H_a\)[/tex]) would be: [tex]\(\mu > 19500\)[/tex].
3. Choosing the Correct Option:
Among the choices provided, the correct null and alternate hypothesis pair matches the option where:
[tex]\[
H_0: \mu = 19500 \quad \text{and} \quad H_a: \mu > 19500
\][/tex]
With this understanding, we see that Alyssa's claim is captured by testing whether the mean price is greater than the population average, reflecting a more fashion-conscious spending in her school.
1. Understanding the Hypotheses:
- Null Hypothesis ([tex]\(H_0\)[/tex]): This hypothesis represents the status quo or a baseline that Alyssa wants to test against. In this case, it is the claim that the mean price of a prom dress in her school is equal to the population mean, which is [tex]$19,500.
- Alternate Hypothesis (\(H_a\)): This hypothesis represents Alyssa's belief or what she thinks could be true. Alyssa believes that her school's students spend more on prom dresses than the average. Therefore, the alternate hypothesis would be that the mean price of a prom dress in her school is greater than $[/tex]19,500.
2. Formulating the Hypotheses:
- The Null Hypothesis ([tex]\(H_0\)[/tex]) would be: [tex]\(\mu = 19500\)[/tex].
- The Alternate Hypothesis ([tex]\(H_a\)[/tex]) would be: [tex]\(\mu > 19500\)[/tex].
3. Choosing the Correct Option:
Among the choices provided, the correct null and alternate hypothesis pair matches the option where:
[tex]\[
H_0: \mu = 19500 \quad \text{and} \quad H_a: \mu > 19500
\][/tex]
With this understanding, we see that Alyssa's claim is captured by testing whether the mean price is greater than the population average, reflecting a more fashion-conscious spending in her school.
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