The 99% confidence interval for the mean high temperature of the sample data is (97.02, 98.58), indicating with 99% confidence that the true population mean falls within this range of temperatures.
To calculate the 99% confidence interval of the mean high temperature of the sample data. Here are the steps to do that:
Find the sample size, mean, and standard deviation of the data. You can use a calculator or a spreadsheet to do this. The values are:
Sample size: n = 7
Sample mean:
= 97.8
Sample standard deviation: s = 0.8
Choose the confidence level. In this case, it is 99%, which corresponds to a z-value of 2.58. You can find the z-value from a table or a calculator.
Use the formula for the confidence interval of the mean:
Confidence Interval =
+/- z * (s/√n)
Plug in the values and simplify:
Confidence Interval = 97.8 +/- 2.58 * (0.8/√7)
Confidence Interval = 97.8 +/- 0.78
Confidence Interval = (97.02, 98.58)
Write the answer as an open interval using parentheses:
(97.02, 98.58)
This is the 99% confidence interval of the mean high temperature of the sample data. It means that we are 99% confident that the true population mean of the high temperatures is between 97.02 and 98.58 degrees Fahrenheit.