Answer :
To solve this question, we need to determine the correct null and alternative hypotheses based on Alyssa's claim about the mean price of prom dresses at her school.
### Step 1: Understand the Situation
- The average price of a prom dress, according to a survey, is [tex]$195.00 with a standard deviation of $[/tex]12.00.
- Alyssa believes that prom dresses at her school are more expensive, specifically greater than [tex]$195.00.
- She collects data from 20 students and finds an average price of $[/tex]208.00.
### Step 2: Formulate Hypotheses
When setting up hypotheses, the null hypothesis (H₀) often states that there is no effect or no difference, while the alternative hypothesis (Hₐ) is what you're trying to find evidence for.
#### Null Hypothesis (H₀)
- The null hypothesis would be that the mean price of a prom dress at Alyssa's school is equal to the survey's mean, which is [tex]$195. This is a statement of "no change" or "no difference."
\( H_0: \mu = 195 \)
#### Alternative Hypothesis (Hₐ)
- Alyssa's claim is that the prom dresses are more expensive at her school, implying that the average is greater than $[/tex]195.
[tex]\( H_a: \mu > 195 \)[/tex]
### Conclusion
Based on Alyssa's belief and the data she collected, the correct hypotheses are:
- Null Hypothesis: [tex]\( H_0: \mu = 195 \)[/tex]
- Alternative Hypothesis: [tex]\( H_a: \mu > 195 \)[/tex]
Thus, the correct option is:
- [tex]\( H_0: \mu = 195; H_a: \mu > 195 \)[/tex]
This means the survey's average is taken as the baseline, and Alyssa is testing to see if her school's average is statistically greater than that baseline.
### Step 1: Understand the Situation
- The average price of a prom dress, according to a survey, is [tex]$195.00 with a standard deviation of $[/tex]12.00.
- Alyssa believes that prom dresses at her school are more expensive, specifically greater than [tex]$195.00.
- She collects data from 20 students and finds an average price of $[/tex]208.00.
### Step 2: Formulate Hypotheses
When setting up hypotheses, the null hypothesis (H₀) often states that there is no effect or no difference, while the alternative hypothesis (Hₐ) is what you're trying to find evidence for.
#### Null Hypothesis (H₀)
- The null hypothesis would be that the mean price of a prom dress at Alyssa's school is equal to the survey's mean, which is [tex]$195. This is a statement of "no change" or "no difference."
\( H_0: \mu = 195 \)
#### Alternative Hypothesis (Hₐ)
- Alyssa's claim is that the prom dresses are more expensive at her school, implying that the average is greater than $[/tex]195.
[tex]\( H_a: \mu > 195 \)[/tex]
### Conclusion
Based on Alyssa's belief and the data she collected, the correct hypotheses are:
- Null Hypothesis: [tex]\( H_0: \mu = 195 \)[/tex]
- Alternative Hypothesis: [tex]\( H_a: \mu > 195 \)[/tex]
Thus, the correct option is:
- [tex]\( H_0: \mu = 195; H_a: \mu > 195 \)[/tex]
This means the survey's average is taken as the baseline, and Alyssa is testing to see if her school's average is statistically greater than that baseline.
