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Answer :
To address this question, we need to set up the null and alternative hypotheses properly based on the scenario provided:
Context:
- The mean price of a prom dress according to a survey is [tex]$195.00 with a standard deviation of $[/tex]12.00.
- Alyssa suspects that students at her high school spend more than [tex]$195.00 on prom dresses, and she conducted a sample survey resulting in an average price of $[/tex]208.00.
Hypotheses:
1. Null Hypothesis (H₀): This is the statement that there is no effect or no difference, and it represents the status quo. Here, it suggests that the mean price of prom dresses is [tex]$195.00. This is written as \( H_0: \mu = 195 \).
2. Alternative Hypothesis (Hₐ): This reflects Alyssa's belief or claim. She thinks that the mean price at her school is greater than $[/tex]195.00. Therefore, the alternative hypothesis is [tex]\( H_a: \mu > 195 \)[/tex].
Given these explanations, the correct hypothesis set is:
- [tex]\( H_0: \mu = 195 \)[/tex]
- [tex]\( H_a: \mu > 195 \)[/tex]
This matches the option:
- [tex]\( H_0: \mu = 195 ; H_a: \mu > 195 \)[/tex]
In hypothesis testing, we test the null hypothesis against the alternative hypothesis. If the data provides sufficient evidence to support the alternative hypothesis, we reject the null hypothesis in favor of the alternative. In this case, Alyssa's sample findings suggest that the actual average could indeed be higher than $195.00, supporting her hypothesis.
Context:
- The mean price of a prom dress according to a survey is [tex]$195.00 with a standard deviation of $[/tex]12.00.
- Alyssa suspects that students at her high school spend more than [tex]$195.00 on prom dresses, and she conducted a sample survey resulting in an average price of $[/tex]208.00.
Hypotheses:
1. Null Hypothesis (H₀): This is the statement that there is no effect or no difference, and it represents the status quo. Here, it suggests that the mean price of prom dresses is [tex]$195.00. This is written as \( H_0: \mu = 195 \).
2. Alternative Hypothesis (Hₐ): This reflects Alyssa's belief or claim. She thinks that the mean price at her school is greater than $[/tex]195.00. Therefore, the alternative hypothesis is [tex]\( H_a: \mu > 195 \)[/tex].
Given these explanations, the correct hypothesis set is:
- [tex]\( H_0: \mu = 195 \)[/tex]
- [tex]\( H_a: \mu > 195 \)[/tex]
This matches the option:
- [tex]\( H_0: \mu = 195 ; H_a: \mu > 195 \)[/tex]
In hypothesis testing, we test the null hypothesis against the alternative hypothesis. If the data provides sufficient evidence to support the alternative hypothesis, we reject the null hypothesis in favor of the alternative. In this case, Alyssa's sample findings suggest that the actual average could indeed be higher than $195.00, supporting her hypothesis.
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