IDNLearn.com is your go-to resource for finding precise and accurate answers. Our Q&A platform offers reliable and thorough answers to ensure you have the information you need to succeed in any situation.
Sagot :
Let's go through the steps to solve this problem:
### 1) Determine the null and alternative hypotheses.
We want to determine if the proportion of people who experienced dizziness varies between different treatment groups.
- Null Hypothesis [tex]\(H_0\)[/tex]: The proportion of people within each treatment group who experienced dizziness is the same.
- Alternative Hypothesis [tex]\(H_a\)[/tex]: The proportion of people within each treatment group who experienced dizziness is different.
Therefore, the correct pair of hypotheses is:
[tex]\[ H_0 : \text{The proportion of people within each treatment group who experienced dizziness are the same} \][/tex]
[tex]\[ H_a : \text{The proportion of people within each treatment group who experienced dizziness are different} \][/tex]
### 2) Determine the test statistic.
The test statistic used here is the Chi-Square statistic. The Chi-Square statistic is calculated as:
[tex]\[ \chi^2 = 4.67 \][/tex]
### 3) Determine the p-value.
The p-value associated with the test statistic is a measure of the probability that the observed differences occurred by chance alone under the null hypothesis. The p-value calculated is:
[tex]\[ \text{P-value} = 0.3226 \][/tex]
### 4) Make a decision.
To make a decision, we compare the p-value to the significance level, [tex]\(\alpha\)[/tex]. Typically, [tex]\(\alpha\)[/tex] is set at 0.05 (5%).
- If the p-value is less than [tex]\(\alpha\)[/tex], we reject the null hypothesis.
- If the p-value is greater than or equal to [tex]\(\alpha\)[/tex], we fail to reject the null hypothesis.
In this case, the p-value is 0.3226, which is greater than 0.05. Hence, we fail to reject the null hypothesis.
### Decision:
Based on the p-value, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the proportion of people who experienced dizziness differs significantly among the treatment groups.
### 1) Determine the null and alternative hypotheses.
We want to determine if the proportion of people who experienced dizziness varies between different treatment groups.
- Null Hypothesis [tex]\(H_0\)[/tex]: The proportion of people within each treatment group who experienced dizziness is the same.
- Alternative Hypothesis [tex]\(H_a\)[/tex]: The proportion of people within each treatment group who experienced dizziness is different.
Therefore, the correct pair of hypotheses is:
[tex]\[ H_0 : \text{The proportion of people within each treatment group who experienced dizziness are the same} \][/tex]
[tex]\[ H_a : \text{The proportion of people within each treatment group who experienced dizziness are different} \][/tex]
### 2) Determine the test statistic.
The test statistic used here is the Chi-Square statistic. The Chi-Square statistic is calculated as:
[tex]\[ \chi^2 = 4.67 \][/tex]
### 3) Determine the p-value.
The p-value associated with the test statistic is a measure of the probability that the observed differences occurred by chance alone under the null hypothesis. The p-value calculated is:
[tex]\[ \text{P-value} = 0.3226 \][/tex]
### 4) Make a decision.
To make a decision, we compare the p-value to the significance level, [tex]\(\alpha\)[/tex]. Typically, [tex]\(\alpha\)[/tex] is set at 0.05 (5%).
- If the p-value is less than [tex]\(\alpha\)[/tex], we reject the null hypothesis.
- If the p-value is greater than or equal to [tex]\(\alpha\)[/tex], we fail to reject the null hypothesis.
In this case, the p-value is 0.3226, which is greater than 0.05. Hence, we fail to reject the null hypothesis.
### Decision:
Based on the p-value, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the proportion of people who experienced dizziness differs significantly among the treatment groups.
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.