Thank you for visiting You wish to test the following claim tex H a tex at a significance level of tex alpha 0 05 tex tex begin array l. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To test the claim [tex]\(H_a: \mu_1 < \mu_2\)[/tex] at a significance level of [tex]\(\alpha = 0.05\)[/tex], using two samples of data, follow these steps:
1. State the Hypotheses:
- Null Hypothesis ([tex]\(H_0\)[/tex]): [tex]\(\mu_1 = \mu_2\)[/tex]
- Alternative Hypothesis ([tex]\(H_a\)[/tex]): [tex]\(\mu_1 < \mu_2\)[/tex]
2. Collect Sample Data:
- Sample 1: Composed of 52 data points.
- Sample 2: Composed of 46 data points.
3. Calculate Sample Means and Standard Deviations:
- For Sample 1, compute the mean and standard deviation.
- For Sample 2, compute the mean and standard deviation.
4. Compute the Standard Error of Difference (SED):
[tex]\[
\text{SED} = \sqrt{\left(\frac{\text{std1}^2}{n1}\right) + \left(\frac{\text{std2}^2}{n2}\right)}
\][/tex]
where [tex]\(\text{std1}\)[/tex] and [tex]\(\text{std2}\)[/tex] are the standard deviations of Sample 1 and Sample 2, respectively, and [tex]\(n1\)[/tex] and [tex]\(n2\)[/tex] are their sizes.
5. Calculate the Test Statistic:
[tex]\[
t = \frac{\text{mean1} - \text{mean2}}{\text{SED}}
\][/tex]
6. Determine Degrees of Freedom (df):
- The degrees of freedom are determined to be equal to the smaller of [tex]\(n1 - 1\)[/tex] and [tex]\(n2 - 1\)[/tex].
7. Find the p-value:
- Using the calculated [tex]\(t\)[/tex]-statistic and degrees of freedom, find the [tex]\(p\)[/tex]-value from the [tex]\(t\)[/tex]-distribution for a one-tailed test.
Here is the result for this specific test:
- Test Statistic: [tex]\(-2.437\)[/tex]
- p-value: [tex]\(0.0094\)[/tex]
Conclusion:
Since the p-value ([tex]\(0.0094\)[/tex]) is less than the significance level ([tex]\(\alpha = 0.05\)[/tex]), we reject the null hypothesis [tex]\(H_0\)[/tex]. There is significant evidence to support the claim that [tex]\(\mu_1 < \mu_2\)[/tex].
1. State the Hypotheses:
- Null Hypothesis ([tex]\(H_0\)[/tex]): [tex]\(\mu_1 = \mu_2\)[/tex]
- Alternative Hypothesis ([tex]\(H_a\)[/tex]): [tex]\(\mu_1 < \mu_2\)[/tex]
2. Collect Sample Data:
- Sample 1: Composed of 52 data points.
- Sample 2: Composed of 46 data points.
3. Calculate Sample Means and Standard Deviations:
- For Sample 1, compute the mean and standard deviation.
- For Sample 2, compute the mean and standard deviation.
4. Compute the Standard Error of Difference (SED):
[tex]\[
\text{SED} = \sqrt{\left(\frac{\text{std1}^2}{n1}\right) + \left(\frac{\text{std2}^2}{n2}\right)}
\][/tex]
where [tex]\(\text{std1}\)[/tex] and [tex]\(\text{std2}\)[/tex] are the standard deviations of Sample 1 and Sample 2, respectively, and [tex]\(n1\)[/tex] and [tex]\(n2\)[/tex] are their sizes.
5. Calculate the Test Statistic:
[tex]\[
t = \frac{\text{mean1} - \text{mean2}}{\text{SED}}
\][/tex]
6. Determine Degrees of Freedom (df):
- The degrees of freedom are determined to be equal to the smaller of [tex]\(n1 - 1\)[/tex] and [tex]\(n2 - 1\)[/tex].
7. Find the p-value:
- Using the calculated [tex]\(t\)[/tex]-statistic and degrees of freedom, find the [tex]\(p\)[/tex]-value from the [tex]\(t\)[/tex]-distribution for a one-tailed test.
Here is the result for this specific test:
- Test Statistic: [tex]\(-2.437\)[/tex]
- p-value: [tex]\(0.0094\)[/tex]
Conclusion:
Since the p-value ([tex]\(0.0094\)[/tex]) is less than the significance level ([tex]\(\alpha = 0.05\)[/tex]), we reject the null hypothesis [tex]\(H_0\)[/tex]. There is significant evidence to support the claim that [tex]\(\mu_1 < \mu_2\)[/tex].
Thank you for reading the article You wish to test the following claim tex H a tex at a significance level of tex alpha 0 05 tex tex begin array l. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
