Answer :
To determine the correct null and alternate hypotheses for this problem, let's break down the information:
1. Understanding the Question:
Alyssa believes that students at her school spend more than [tex]$195 on prom dresses. To test her belief, we need to set up hypotheses comparing the mean prices.
2. Setting Up Hypotheses:
- Null Hypothesis (H₀): This is the statement we initially assume to be true or the status quo. In this context, we assume that the average amount spent is equal to $[/tex]195. Therefore, [tex]\( H_0: \mu = 195 \)[/tex].
- Alternative Hypothesis (Hₐ): This represents what Alyssa wants to test or prove. Since she believes students spend more, the alternative hypothesis is that the average spending is greater than [tex]$195. Thus, \( H_a: \mu > 195 \).
3. Reviewing Options:
- \( H_0: \mu = 195 \); \( H_a: \mu > 195 \) (This matches Alyssa's belief.)
- \( H_0: \mu \neq 195 \); \( H_a: \mu = 208 \) (This is inconsistent as it doesn't directly relate to her belief that students spend more than $[/tex]195.)
- [tex]\( H_0: \mu = 195 \)[/tex]; [tex]\( H_a: \mu = 195 \)[/tex] (This isn't a valid test as both hypotheses are the same.)
- [tex]\( H_0: \mu < 195 \)[/tex]; [tex]\( H_a: \mu \geq 208 \)[/tex] (This contradicts the hypothesis test we need, where we are checking if the mean is greater than $195.)
Therefore, the correct hypotheses reflecting Alyssa's claim are:
Null Hypothesis (H₀): [tex]\(\mu = 195\)[/tex]
Alternative Hypothesis (Hₐ): [tex]\(\mu > 195\)[/tex]
1. Understanding the Question:
Alyssa believes that students at her school spend more than [tex]$195 on prom dresses. To test her belief, we need to set up hypotheses comparing the mean prices.
2. Setting Up Hypotheses:
- Null Hypothesis (H₀): This is the statement we initially assume to be true or the status quo. In this context, we assume that the average amount spent is equal to $[/tex]195. Therefore, [tex]\( H_0: \mu = 195 \)[/tex].
- Alternative Hypothesis (Hₐ): This represents what Alyssa wants to test or prove. Since she believes students spend more, the alternative hypothesis is that the average spending is greater than [tex]$195. Thus, \( H_a: \mu > 195 \).
3. Reviewing Options:
- \( H_0: \mu = 195 \); \( H_a: \mu > 195 \) (This matches Alyssa's belief.)
- \( H_0: \mu \neq 195 \); \( H_a: \mu = 208 \) (This is inconsistent as it doesn't directly relate to her belief that students spend more than $[/tex]195.)
- [tex]\( H_0: \mu = 195 \)[/tex]; [tex]\( H_a: \mu = 195 \)[/tex] (This isn't a valid test as both hypotheses are the same.)
- [tex]\( H_0: \mu < 195 \)[/tex]; [tex]\( H_a: \mu \geq 208 \)[/tex] (This contradicts the hypothesis test we need, where we are checking if the mean is greater than $195.)
Therefore, the correct hypotheses reflecting Alyssa's claim are:
Null Hypothesis (H₀): [tex]\(\mu = 195\)[/tex]
Alternative Hypothesis (Hₐ): [tex]\(\mu > 195\)[/tex]
