Answer :
Sure, let's go through the process of determining the null and alternative hypotheses for the given scenario.
Alyssa believes that students at her school spend more on prom dresses than the reported average price of [tex]$195. Here's how we formulate the hypotheses:
1. Null Hypothesis (\(H_0\)): The null hypothesis generally represents a statement of no effect or no difference. For this problem, it should express the idea that there is no difference in mean prom dress price compared to the average recorded price. So, the null hypothesis is:
- \(H_0: \mu = 195\)
This hypothesis assumes that the mean price of prom dresses at Alyssa’s school is $[/tex]195, the same as the national average or expected price.
2. Alternative Hypothesis ([tex]\(H_a\)[/tex]): The alternative hypothesis represents the statement we want to test. Alyssa thinks that the prom dresses at her school are more expensive. Therefore, her initial assertion implies that the average price is different from [tex]$195. The alternative hypothesis can be stated as:
- \(H_a: \mu \neq 195\)
This indicates that the mean prom dress price at Alyssa’s school differs from $[/tex]195. Given the choices, this matches her belief more generally that the price could be higher, but does not specify a single direction (greater or lesser).
Thus, based on the options presented:
- [tex]\(H_0: \mu = 195\)[/tex]
- [tex]\(H_a: \mu \neq 195\)[/tex]
This option states that we are testing whether the mean price is any different from $195. This is the appropriate hypothesis test to see if Alyssa’s school really spends differently on prom dresses compared to the expected average.
Alyssa believes that students at her school spend more on prom dresses than the reported average price of [tex]$195. Here's how we formulate the hypotheses:
1. Null Hypothesis (\(H_0\)): The null hypothesis generally represents a statement of no effect or no difference. For this problem, it should express the idea that there is no difference in mean prom dress price compared to the average recorded price. So, the null hypothesis is:
- \(H_0: \mu = 195\)
This hypothesis assumes that the mean price of prom dresses at Alyssa’s school is $[/tex]195, the same as the national average or expected price.
2. Alternative Hypothesis ([tex]\(H_a\)[/tex]): The alternative hypothesis represents the statement we want to test. Alyssa thinks that the prom dresses at her school are more expensive. Therefore, her initial assertion implies that the average price is different from [tex]$195. The alternative hypothesis can be stated as:
- \(H_a: \mu \neq 195\)
This indicates that the mean prom dress price at Alyssa’s school differs from $[/tex]195. Given the choices, this matches her belief more generally that the price could be higher, but does not specify a single direction (greater or lesser).
Thus, based on the options presented:
- [tex]\(H_0: \mu = 195\)[/tex]
- [tex]\(H_a: \mu \neq 195\)[/tex]
This option states that we are testing whether the mean price is any different from $195. This is the appropriate hypothesis test to see if Alyssa’s school really spends differently on prom dresses compared to the expected average.
