Thank you for visiting The body temperatures in degrees Fahrenheit of a sample of adults in one small town are 98 97 9 99 97 3 98 9 99. 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 :
The 95% confidence interval of the mean body temperature of adults in the town is (97.584, 98.876)°F (open-interval notation), accurate to 3 decimal places.
What is the 95% confidence interval of the mean body temperature of adults in the town?
To find the 95% confidence interval (C.I.) of the mean body temperature, we need to use the formula:
C.I. = x ± z*(σ/√n)
Where:
x is the sample mean
σ is the population standard deviation (unknown, but we can estimate it using the sample standard deviation)
n is the sample size
z is the critical value for the desired confidence level (95% in this case)
First, we need to calculate the sample mean, sample standard deviation, and sample size:
x = (98 + 97.9 + 99 + 97.3 + 98.9 + 99.6 + 97.8 + 99.8 + 99.1 + 98.4 + 98.7 + 97.6 + 96.5) / 13 = 98.23
s = √((1/(n-1)) * Σ(xi - x)²)
s = 1.339
n = 13
Next, we need to find the critical value, z, for a 95% confidence level. We can look this up in a standard normal distribution table or use a calculator. For a 95% confidence level, z = 1.96.
Now we can plug in the values into the formula to get the 95% confidence interval:
C.I. = 98.23 ± 1.96*(1.339/√13) = (97.584, 98.876)
Learn more about confidence intervals at: https://brainly.com/question/17097944
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