Thank you for visiting In this scenario what is the test statistic It is commonly known that the average body temperature for adults is 98 6 degrees Fahrenheit Sample. 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 calculate the test statistic for this problem, we use the provided formula for the test statistic [tex]\( z_0 \)[/tex]:
[tex]\[ z_0 = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}} \][/tex]
Let's break down each part of the formula using the given values:
- [tex]\(\bar{x}\)[/tex] is the sample mean, which is 99.8 degrees Fahrenheit.
- [tex]\(\mu_0\)[/tex] is the population mean under the null hypothesis, which is 98.6 degrees Fahrenheit.
- [tex]\(\sigma\)[/tex] is the population standard deviation, known to be 15 degrees Fahrenheit.
- [tex]\(n\)[/tex] is the sample size, which is 40.
Now, substitute these values into the formula:
1. Calculate the difference between the sample mean and the population mean:
[tex]\(\bar{x} - \mu_0 = 99.8 - 98.6 = 1.2\)[/tex]
2. Calculate the standard error of the mean, which involves dividing the population standard deviation by the square root of the sample size:
[tex]\(\frac{\sigma}{\sqrt{n}} = \frac{15}{\sqrt{40}}\)[/tex]
3. Calculate the test statistic [tex]\( z_0 \)[/tex]:
[tex]\[ z_0 = \frac{1.2}{\frac{15}{\sqrt{40}}} \][/tex]
4. Simplify the calculation to find [tex]\( z_0 \)[/tex]:
Perform the division:
[tex]\(\frac{15}{\sqrt{40}} \approx 2.3717\)[/tex]
Now, divide the difference in means by the standard error:
[tex]\[ z_0 = \frac{1.2}{2.3717} \approx 0.5059644256269419 \][/tex]
5. Finally, round [tex]\( z_0 \)[/tex] to two decimal places to get the final answer:
[tex]\( z_0 \approx 0.51 \)[/tex]
So, the test statistic [tex]\( z_0 \)[/tex] is approximately 0.51.
[tex]\[ z_0 = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}} \][/tex]
Let's break down each part of the formula using the given values:
- [tex]\(\bar{x}\)[/tex] is the sample mean, which is 99.8 degrees Fahrenheit.
- [tex]\(\mu_0\)[/tex] is the population mean under the null hypothesis, which is 98.6 degrees Fahrenheit.
- [tex]\(\sigma\)[/tex] is the population standard deviation, known to be 15 degrees Fahrenheit.
- [tex]\(n\)[/tex] is the sample size, which is 40.
Now, substitute these values into the formula:
1. Calculate the difference between the sample mean and the population mean:
[tex]\(\bar{x} - \mu_0 = 99.8 - 98.6 = 1.2\)[/tex]
2. Calculate the standard error of the mean, which involves dividing the population standard deviation by the square root of the sample size:
[tex]\(\frac{\sigma}{\sqrt{n}} = \frac{15}{\sqrt{40}}\)[/tex]
3. Calculate the test statistic [tex]\( z_0 \)[/tex]:
[tex]\[ z_0 = \frac{1.2}{\frac{15}{\sqrt{40}}} \][/tex]
4. Simplify the calculation to find [tex]\( z_0 \)[/tex]:
Perform the division:
[tex]\(\frac{15}{\sqrt{40}} \approx 2.3717\)[/tex]
Now, divide the difference in means by the standard error:
[tex]\[ z_0 = \frac{1.2}{2.3717} \approx 0.5059644256269419 \][/tex]
5. Finally, round [tex]\( z_0 \)[/tex] to two decimal places to get the final answer:
[tex]\( z_0 \approx 0.51 \)[/tex]
So, the test statistic [tex]\( z_0 \)[/tex] is approximately 0.51.
Thank you for reading the article In this scenario what is the test statistic It is commonly known that the average body temperature for adults is 98 6 degrees Fahrenheit Sample. 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
