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Answer :
To determine the correct null and alternative hypotheses for Alyssa's situation, let's begin by understanding what her objective is. She believes that students in her high school spent more on prom dresses than the average reported in the survey, which was [tex]$195.
### Step 1: Define the Null Hypothesis (H₀)
The null hypothesis is a statement of no effect or no difference. It reflects the situation of the general population as per the given information or assumption. In this context, the null hypothesis would state that the mean price of a prom dress for her school is the same as the broader survey's mean.
- Null Hypothesis (H₀): The mean price of a prom dress at Alyssa's school is $[/tex]195.
- Mathematically, [tex]\( H_0: \mu = 195 \)[/tex].
### Step 2: Define the Alternative Hypothesis (Hₐ)
The alternative hypothesis is what Alyssa is trying to prove. It suggests that there is a difference or effect—in this case, that the mean price of prom dresses at her school is greater than the mean reported in the survey.
- Alternative Hypothesis (Hₐ): The mean price of a prom dress at Alyssa's school is greater than $195.
- Mathematically, [tex]\( H_a: \mu > 195 \)[/tex].
Given this understanding, the correct set of hypotheses for testing her belief is:
- [tex]\( H_0: \mu = 195 \)[/tex]
- [tex]\( H_a: \mu > 195 \)[/tex]
Therefore, the first choice provided in the options is the correct one:
- [tex]\( H_0: \mu=195 \)[/tex]; [tex]\( H_a: \mu>195 \)[/tex]
### Step 1: Define the Null Hypothesis (H₀)
The null hypothesis is a statement of no effect or no difference. It reflects the situation of the general population as per the given information or assumption. In this context, the null hypothesis would state that the mean price of a prom dress for her school is the same as the broader survey's mean.
- Null Hypothesis (H₀): The mean price of a prom dress at Alyssa's school is $[/tex]195.
- Mathematically, [tex]\( H_0: \mu = 195 \)[/tex].
### Step 2: Define the Alternative Hypothesis (Hₐ)
The alternative hypothesis is what Alyssa is trying to prove. It suggests that there is a difference or effect—in this case, that the mean price of prom dresses at her school is greater than the mean reported in the survey.
- Alternative Hypothesis (Hₐ): The mean price of a prom dress at Alyssa's school is greater than $195.
- Mathematically, [tex]\( H_a: \mu > 195 \)[/tex].
Given this understanding, the correct set of hypotheses for testing her belief is:
- [tex]\( H_0: \mu = 195 \)[/tex]
- [tex]\( H_a: \mu > 195 \)[/tex]
Therefore, the first choice provided in the options is the correct one:
- [tex]\( H_0: \mu=195 \)[/tex]; [tex]\( H_a: \mu>195 \)[/tex]
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