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Answer :
To solve this question, we need to formulate the null and alternate hypotheses based on the problem statement and Alyssa's claim.
### Step-by-Step Solution:
1. Understand the Problem:
- The mean price of a prom dress from a survey of 8,000 high school students is [tex]$\$[/tex]195.00[tex]$.
- Alyssa believes that students at her school spend more than this average price, suggesting a mean greater than $[/tex]\[tex]$195.00$[/tex].
2. Define the Null Hypothesis (H₀):
- The null hypothesis typically states that there is no effect or no difference. In this case, it would suggest that the mean price of prom dresses in Alyssa's school is the same as the general surveyed mean.
- H₀: μ = 195
- This means the average prom dress price at Alyssa's school is equal to [tex]$\$[/tex]195.00[tex]$.
3. Define the Alternate Hypothesis (Hₐ):
- The alternate hypothesis is what you want to prove. Alyssa thinks that the students at her high school spend more, which points towards a mean greater than the general surveyed mean.
- Hₐ: μ > 195
- This means the average prom dress price at Alyssa's school is more than $[/tex]\[tex]$195.00$[/tex].
4. Compare with Given Choices:
- Looking at the given options, the correct null hypothesis (H₀) and alternate hypothesis (Hₐ) that align with Alyssa's claim are:
- [tex]\(H _0: \mu = 195\)[/tex]; [tex]\(H _{ a }: \mu > 195\)[/tex]
This pair correctly reflects the situation presented: Alyssa's belief that the mean price at her school is greater than the general mean from the survey.
### Step-by-Step Solution:
1. Understand the Problem:
- The mean price of a prom dress from a survey of 8,000 high school students is [tex]$\$[/tex]195.00[tex]$.
- Alyssa believes that students at her school spend more than this average price, suggesting a mean greater than $[/tex]\[tex]$195.00$[/tex].
2. Define the Null Hypothesis (H₀):
- The null hypothesis typically states that there is no effect or no difference. In this case, it would suggest that the mean price of prom dresses in Alyssa's school is the same as the general surveyed mean.
- H₀: μ = 195
- This means the average prom dress price at Alyssa's school is equal to [tex]$\$[/tex]195.00[tex]$.
3. Define the Alternate Hypothesis (Hₐ):
- The alternate hypothesis is what you want to prove. Alyssa thinks that the students at her high school spend more, which points towards a mean greater than the general surveyed mean.
- Hₐ: μ > 195
- This means the average prom dress price at Alyssa's school is more than $[/tex]\[tex]$195.00$[/tex].
4. Compare with Given Choices:
- Looking at the given options, the correct null hypothesis (H₀) and alternate hypothesis (Hₐ) that align with Alyssa's claim are:
- [tex]\(H _0: \mu = 195\)[/tex]; [tex]\(H _{ a }: \mu > 195\)[/tex]
This pair correctly reflects the situation presented: Alyssa's belief that the mean price at her school is greater than the general mean from the survey.
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