We appreciate your visit to A random sample of 10 independent healthy people showed the body temperatures given below in degrees Fahrenheit Test the hypothesis that the population mean is. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To solve this problem, we need to test the hypothesis regarding the mean body temperature of a population based on a sample. Here is how you can approach the problem step-by-step:
### Step 1: Set the Hypotheses
We need to determine the null and alternative hypotheses:
- Null Hypothesis ([tex]\(H_0\)[/tex]): The population mean [tex]\(\mu\)[/tex] is equal to 98.6°F.
- Alternative Hypothesis ([tex]\(H_a\)[/tex]): The population mean [tex]\(\mu\)[/tex] is not equal to 98.6°F.
Thus, we choose:
[tex]\(H_0: \mu = 98.6\)[/tex]
[tex]\(H_a: \mu \neq 98.6\)[/tex]
This corresponds to a two-tailed test.
### Step 2: Check Conditions
Before proceeding with the t-test, we should confirm the conditions:
- The sample is random, and the observations are independent.
- The distribution of the population is approximately Normal.
Since these conditions are mentioned as fulfilled in the problem, we can proceed with the t-test.
### Step 3: Calculate the Test Statistic
1. Sample Data:
The sample consists of body temperatures:
[tex]\[ 98.5, 98.2, 99.0, 96.3, 98.7, 98.7, 97.1, 99.1, 98.3, 97.6 \][/tex]
2. Sample Size ([tex]\(n\)[/tex]):
The sample size is 10.
3. Sample Mean ([tex]\(\bar{x}\)[/tex]):
Calculate the mean of the sample data.
4. Sample Standard Deviation ([tex]\(s\)[/tex]):
Calculate the standard deviation of the sample using Bessel's correction ([tex]\(ddof=1\)[/tex]).
5. Calculate the t-statistic:
Use the formula:
[tex]\[ t = \frac{\bar{x} - 98.6}{s/\sqrt{n}} \][/tex]
The calculation results in a t-statistic of approximately [tex]\(-1.59\)[/tex].
### Conclusion
With the calculated t-statistic in hand, you can compare it to the critical t-value from the t-distribution table (based on the degree of freedom [tex]\(n-1\)[/tex] and the significance level 0.05) to conclude whether to reject or fail to reject the null hypothesis. Since the problem only asks us to find the test statistic, we stop here. The correct choice of hypotheses based on the given options is:
F. [tex]\(H_0: \mu = 98.6\)[/tex], [tex]\(H_a: \mu \neq 98.6\)[/tex].
### Step 1: Set the Hypotheses
We need to determine the null and alternative hypotheses:
- Null Hypothesis ([tex]\(H_0\)[/tex]): The population mean [tex]\(\mu\)[/tex] is equal to 98.6°F.
- Alternative Hypothesis ([tex]\(H_a\)[/tex]): The population mean [tex]\(\mu\)[/tex] is not equal to 98.6°F.
Thus, we choose:
[tex]\(H_0: \mu = 98.6\)[/tex]
[tex]\(H_a: \mu \neq 98.6\)[/tex]
This corresponds to a two-tailed test.
### Step 2: Check Conditions
Before proceeding with the t-test, we should confirm the conditions:
- The sample is random, and the observations are independent.
- The distribution of the population is approximately Normal.
Since these conditions are mentioned as fulfilled in the problem, we can proceed with the t-test.
### Step 3: Calculate the Test Statistic
1. Sample Data:
The sample consists of body temperatures:
[tex]\[ 98.5, 98.2, 99.0, 96.3, 98.7, 98.7, 97.1, 99.1, 98.3, 97.6 \][/tex]
2. Sample Size ([tex]\(n\)[/tex]):
The sample size is 10.
3. Sample Mean ([tex]\(\bar{x}\)[/tex]):
Calculate the mean of the sample data.
4. Sample Standard Deviation ([tex]\(s\)[/tex]):
Calculate the standard deviation of the sample using Bessel's correction ([tex]\(ddof=1\)[/tex]).
5. Calculate the t-statistic:
Use the formula:
[tex]\[ t = \frac{\bar{x} - 98.6}{s/\sqrt{n}} \][/tex]
The calculation results in a t-statistic of approximately [tex]\(-1.59\)[/tex].
### Conclusion
With the calculated t-statistic in hand, you can compare it to the critical t-value from the t-distribution table (based on the degree of freedom [tex]\(n-1\)[/tex] and the significance level 0.05) to conclude whether to reject or fail to reject the null hypothesis. Since the problem only asks us to find the test statistic, we stop here. The correct choice of hypotheses based on the given options is:
F. [tex]\(H_0: \mu = 98.6\)[/tex], [tex]\(H_a: \mu \neq 98.6\)[/tex].
Thanks for taking the time to read A random sample of 10 independent healthy people showed the body temperatures given below in degrees Fahrenheit Test the hypothesis that the population mean is. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
