Answer :
Certainly! Let's break down the process of forming the correct hypotheses needed to address the question.
Background:
- A large survey of 8,000 high school students found that the average price (mean) of a prom dress was [tex]$195.00.
- Alyssa believes that students at her school spend more on prom dresses because they are more fashion conscious.
- She collected data from 20 students at her school and found that the average price was $[/tex]208.00.
Objective:
- Determine the correct null hypothesis ([tex]\( H_0 \)[/tex]) and alternative hypothesis ([tex]\( H_a \)[/tex]) based on Alyssa's suspicion.
Hypothesis Testing Basics:
1. Null Hypothesis ([tex]\( H_0 \)[/tex]): This is the statement that there is no effect or no difference, and it represents a condition that we aim to test against. In this scenario, it assumes that the average price of prom dresses in Alyssa's school is not more than the general average.
2. Alternative Hypothesis ([tex]\( H_a \)[/tex]): This hypothesis reflects what we suspect might be true—in Alyssa's case, she believes her school spends more.
Forming the Hypotheses:
- [tex]\( H_0: \mu = 195 \)[/tex]: This null hypothesis claims that the mean price of a prom dress for Alyssa's school is [tex]$195, which indicates no difference from the general average.
- \( H_a: \mu > 195 \): This alternative hypothesis expresses Alyssa's belief that the mean price is greater than $[/tex]195, based on her data suggesting fashion-conscious students spend more.
Conclusion:
Given Alyssa's suspicion and the data she collected, the correct hypotheses are:
- Null Hypothesis ([tex]\( H_0 \)[/tex]): [tex]\(\mu = 195\)[/tex]
- Alternative Hypothesis ([tex]\( H_a \)[/tex]): [tex]\(\mu > 195\)[/tex]
The correct choice is:
- [tex]\( H_0: \mu=195 ; H_a: \mu>195 \)[/tex]
This setup allows us to test whether there is statistical evidence to support Alyssa's claim that students in her school spend more on prom dresses than the average found in the larger survey.
Background:
- A large survey of 8,000 high school students found that the average price (mean) of a prom dress was [tex]$195.00.
- Alyssa believes that students at her school spend more on prom dresses because they are more fashion conscious.
- She collected data from 20 students at her school and found that the average price was $[/tex]208.00.
Objective:
- Determine the correct null hypothesis ([tex]\( H_0 \)[/tex]) and alternative hypothesis ([tex]\( H_a \)[/tex]) based on Alyssa's suspicion.
Hypothesis Testing Basics:
1. Null Hypothesis ([tex]\( H_0 \)[/tex]): This is the statement that there is no effect or no difference, and it represents a condition that we aim to test against. In this scenario, it assumes that the average price of prom dresses in Alyssa's school is not more than the general average.
2. Alternative Hypothesis ([tex]\( H_a \)[/tex]): This hypothesis reflects what we suspect might be true—in Alyssa's case, she believes her school spends more.
Forming the Hypotheses:
- [tex]\( H_0: \mu = 195 \)[/tex]: This null hypothesis claims that the mean price of a prom dress for Alyssa's school is [tex]$195, which indicates no difference from the general average.
- \( H_a: \mu > 195 \): This alternative hypothesis expresses Alyssa's belief that the mean price is greater than $[/tex]195, based on her data suggesting fashion-conscious students spend more.
Conclusion:
Given Alyssa's suspicion and the data she collected, the correct hypotheses are:
- Null Hypothesis ([tex]\( H_0 \)[/tex]): [tex]\(\mu = 195\)[/tex]
- Alternative Hypothesis ([tex]\( H_a \)[/tex]): [tex]\(\mu > 195\)[/tex]
The correct choice is:
- [tex]\( H_0: \mu=195 ; H_a: \mu>195 \)[/tex]
This setup allows us to test whether there is statistical evidence to support Alyssa's claim that students in her school spend more on prom dresses than the average found in the larger survey.
