Answer :
Sure! Let's break down how to determine the correct null and alternate hypotheses for this situation.
1. Understanding the Context: Alyssa has a hypothesis that students at her school spend more on prom dresses than the average price of [tex]$195 reported from a survey of 8,000 high school students.
2. Null Hypothesis (\(H_0\)): The null hypothesis is a statement that there is no effect or no difference, and it often includes a statement of equality. In this context, the null hypothesis would be that the mean price of a prom dress for Alyssa's school is $[/tex]195. This can be written as:
[tex]\[
H_0: \mu = 195
\][/tex]
3. Alternate Hypothesis ([tex]\(H_a\)[/tex]): The alternate hypothesis is what you are trying to find evidence for. Alyssa believes students at her school spent more than the average [tex]$195. Therefore, the alternate hypothesis should reflect that the mean is greater than 195. This can be expressed as:
\[
H_a: \mu > 195
\]
4. Choosing the Correct Option: By looking at the statements and goals behind the hypotheses, the correct set of hypotheses is:
- Null Hypothesis: \(H_0: \mu = 195\)
- Alternate Hypothesis: \(H_a: \mu > 195\)
This selection reflects that Alyssa wants to test if the mean price is greater than the average reported price of $[/tex]195.
Therefore, the statement [tex]\(H_0: \mu=195 ; H_a: \mu>195\)[/tex] is the correct choice.
1. Understanding the Context: Alyssa has a hypothesis that students at her school spend more on prom dresses than the average price of [tex]$195 reported from a survey of 8,000 high school students.
2. Null Hypothesis (\(H_0\)): The null hypothesis is a statement that there is no effect or no difference, and it often includes a statement of equality. In this context, the null hypothesis would be that the mean price of a prom dress for Alyssa's school is $[/tex]195. This can be written as:
[tex]\[
H_0: \mu = 195
\][/tex]
3. Alternate Hypothesis ([tex]\(H_a\)[/tex]): The alternate hypothesis is what you are trying to find evidence for. Alyssa believes students at her school spent more than the average [tex]$195. Therefore, the alternate hypothesis should reflect that the mean is greater than 195. This can be expressed as:
\[
H_a: \mu > 195
\]
4. Choosing the Correct Option: By looking at the statements and goals behind the hypotheses, the correct set of hypotheses is:
- Null Hypothesis: \(H_0: \mu = 195\)
- Alternate Hypothesis: \(H_a: \mu > 195\)
This selection reflects that Alyssa wants to test if the mean price is greater than the average reported price of $[/tex]195.
Therefore, the statement [tex]\(H_0: \mu=195 ; H_a: \mu>195\)[/tex] is the correct choice.
