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Answer :
To solve the problem, we start by understanding Alyssa's claim. The survey of 8,000 high school students provided a mean prom dress price of \[tex]$195 with a standard deviation of \$[/tex]12. Alyssa believes that her school is more fashion conscious, meaning that students probably spend more than \[tex]$195 on their prom dresses.
In hypothesis testing, we set up the hypotheses as follows:
1. The null hypothesis ($[/tex]H_0[tex]$) represents the status quo or no-effect scenario. In this case, it states that the mean prom dress price is the same as the survey result. Thus,
$[/tex][tex]$ H_0: \mu = 195. $[/tex][tex]$
2. The alternative hypothesis ($[/tex]H_a[tex]$) reflects the claim that we are testing. Since Alyssa's claim is that students at her school spend more than \$[/tex]195, the alternative hypothesis should state that the mean is greater than 195. Thus,
[tex]$$ H_a: \mu > 195. $$[/tex]
This setup clearly matches the option:
[tex]$$ H_0: \mu = 195 \quad ; \quad H_a: \mu > 195. $$[/tex]
Therefore, the correct null and alternate hypotheses are:
- Null hypothesis: [tex]$$ H_0: \mu = 195 $$[/tex]
- Alternative hypothesis: [tex]$$ H_a: \mu > 195 $$[/tex]
This decision corresponds to the first option.
In hypothesis testing, we set up the hypotheses as follows:
1. The null hypothesis ($[/tex]H_0[tex]$) represents the status quo or no-effect scenario. In this case, it states that the mean prom dress price is the same as the survey result. Thus,
$[/tex][tex]$ H_0: \mu = 195. $[/tex][tex]$
2. The alternative hypothesis ($[/tex]H_a[tex]$) reflects the claim that we are testing. Since Alyssa's claim is that students at her school spend more than \$[/tex]195, the alternative hypothesis should state that the mean is greater than 195. Thus,
[tex]$$ H_a: \mu > 195. $$[/tex]
This setup clearly matches the option:
[tex]$$ H_0: \mu = 195 \quad ; \quad H_a: \mu > 195. $$[/tex]
Therefore, the correct null and alternate hypotheses are:
- Null hypothesis: [tex]$$ H_0: \mu = 195 $$[/tex]
- Alternative hypothesis: [tex]$$ H_a: \mu > 195 $$[/tex]
This decision corresponds to the first option.
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