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Answer :
To determine the correct null hypothesis ([tex]\(H_0\)[/tex]) and alternate hypothesis ([tex]\(H_a\)[/tex]), we need to consider Alyssa's belief and what we're testing.
1. Understand the Claim:
Alyssa thinks that students at her high school spend more on prom dresses than the general population average of \[tex]$195.
2. Define the Parameters:
- The population mean for the general survey is \(\mu = 195\).
- Alyssa is suggesting that the mean for her high school \(\mu\) is greater than \$[/tex]195.
3. Set Up the Hypotheses:
- Null Hypothesis ([tex]\(H_0\)[/tex]): This is a statement of no effect or no difference. It represents a standard or baseline level. In this case, it is that the average price of a prom dress in Alyssa's school is equal to the general population average price of \[tex]$195.
\[
H_0: \mu = 195
\]
- Alternate Hypothesis (\(H_a\)): This captures Alyssa's belief or claim about the data, which she wants to test. Here, she thinks that the average price is more than \$[/tex]195.
[tex]\[
H_a: \mu > 195
\][/tex]
Given this setup, the correct hypotheses are:
- [tex]\(H_0: \mu = 195\)[/tex]
- [tex]\(H_a: \mu > 195\)[/tex]
This problem involves a one-tailed test because Alyssa is specifically interested in finding out if the mean price is greater than \$195, not simply different (which would require a two-tailed test).
1. Understand the Claim:
Alyssa thinks that students at her high school spend more on prom dresses than the general population average of \[tex]$195.
2. Define the Parameters:
- The population mean for the general survey is \(\mu = 195\).
- Alyssa is suggesting that the mean for her high school \(\mu\) is greater than \$[/tex]195.
3. Set Up the Hypotheses:
- Null Hypothesis ([tex]\(H_0\)[/tex]): This is a statement of no effect or no difference. It represents a standard or baseline level. In this case, it is that the average price of a prom dress in Alyssa's school is equal to the general population average price of \[tex]$195.
\[
H_0: \mu = 195
\]
- Alternate Hypothesis (\(H_a\)): This captures Alyssa's belief or claim about the data, which she wants to test. Here, she thinks that the average price is more than \$[/tex]195.
[tex]\[
H_a: \mu > 195
\][/tex]
Given this setup, the correct hypotheses are:
- [tex]\(H_0: \mu = 195\)[/tex]
- [tex]\(H_a: \mu > 195\)[/tex]
This problem involves a one-tailed test because Alyssa is specifically interested in finding out if the mean price is greater than \$195, not simply different (which would require a two-tailed test).
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