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Answer :
Answer:
Therefore, the 99% confidence interval of the mean body temperature of adults in the town is (96.180, 98.692) in degrees Fahrenheit.
Explanation:
To find the 99% confidence interval of the mean body temperature of adults in the town, we can follow these steps:
Step 1: Calculate the sample mean.
Add up all the temperatures in the sample and divide by the number of temperatures. In this case, we have 11 temperatures:
97.5 + 99.1 + 97.8 + 98.7 + 96.5 + 97.1 + 99 + 98.9 + 96.7 + 98.3 + 99.2 = 1071.8
Mean = 1071.8 / 11 = 97.436
Step 2: Calculate the standard deviation.
Find the differences between each temperature and the mean, square them, add them up, divide by the sample size minus 1, and then take the square root. Using a calculator, we find the standard deviation to be approximately 1.342.
Step 3: Determine the critical value.
For a 99% confidence interval with a sample size of 11, we can use the t-distribution table or a calculator to find the critical value. The critical value is 3.106.
Step 4: Calculate the margin of error.
The margin of error is the product of the critical value and the standard deviation divided by the square root of the sample size. In this case, it is (3.106 * 1.342) / √11 ≈ 1.256.
Step 5: Calculate the confidence interval.
The confidence interval is the sample mean plus or minus the margin of error. In this case, the 99% confidence interval is approximately (97.436 - 1.256, 97.436 + 1.256), which simplifies to (96.180, 98.692).
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