We appreciate your visit to The body temperatures in degrees Fahrenheit of a sample of adults in one small town are 98 9 96 6 98 6 99 7 97. 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 :
Given the data temperatures to be;
[tex]98.9,96.6,98.6,99.7,97,97.4,99.4[/tex]We would require the following to get the 98% confidence interval of the mean body temperature.
Mean, Standard deviation, sample size, Probability of a confidence interval of 98%.
Using a calculator, we can get the mean to be
[tex]\text{(}\mu)=98.2285[/tex]The standard deviation would be derived to be;
[tex]\sigma=1.2230[/tex]The sample size can be gotten from the question to be;
[tex]n=7[/tex]The probability value of a 98% confidence interval is given to be 2.33
We can then derive the answer using the formula below;
[tex]\mu\pm z^x(\frac{\sigma}{\sqrt[]{n}})[/tex]We would substitute into the formula
[tex]\begin{gathered} \mu\pm z^x(\frac{\sigma}{\sqrt[]{n}}) \\ =98.2285+2.33(\frac{1.2230}{\sqrt[]{7}}) \\ =98.2285\pm1.0770 \\ =(97.152,99.306) \end{gathered}[/tex]ANSWER:
[tex](97.152,99.306)[/tex]Thanks for taking the time to read The body temperatures in degrees Fahrenheit of a sample of adults in one small town are 98 9 96 6 98 6 99 7 97. 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
Final answer:
To find the 98% confidence interval of the mean body temperature, use the t-distribution with the sample mean and standard deviation. Calculate the margin of error and then determine the lower and upper bounds of the confidence interval.
Explanation:
To find the 98% confidence interval of the mean body temperature of adults in the town, we can use the t-distribution since the population standard deviation is unknown. First, calculate the sample mean and standard deviation. In this case, the sample mean is 98.6 degree F and the sample standard deviation is 0.6 degree F. Next, calculate the margin of error by multiplying the critical t-value (obtained from the t-distribution table with the given confidence level and degrees of freedom) with the standard deviation divided by the square root of the sample size. Finally, calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error to the sample mean, respectively.
Sample Mean: 98.6 degree F
Sample Standard Deviation: 0.6 degree F
Critical t-value: Obtain from t-distribution table
Margin of Error: Critical t-value * (Sample Standard Deviation / sqrt(Sample Size))
Lower Bound: Sample Mean - Margin of Error
Upper Bound: Sample Mean + Margin of Error
Learn more about Confidence Intervals here:
https://brainly.com/question/34700241
#SPJ12
