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Confidence Intervals for a Population Mean

Example:
One factor used to determine the reading level a book is sentence length. A random sample of 56 sentences is selected from a new science book. The average sentence length of the sample is 27.8 with a standard deviation of 9.1. Find a 95% confidence interval for the average sentence length in the book. Suppose the population standard deviation is the same as the sample, find the 95% confidence interval for the population mean.

Solution:
First, since you have the mean and standard deviation from one sample, you may use 1- sample t interval to find the confidence interval. From the statistical data list, press "F4" (INTR), then press "F2" (t), and then "F1" (1-S). Because we do not have the original data, we select "F2" (Var) for the data type. Enter the confidence level, sample mean, sample standard deviation, and sample size. Press "F1" (CALC) to get the interval. 

When you want to figure out the confidence interval for the population mean of a sample, you may use 1-sample Z interval. From the statistical data list, press "F4" (INTR), the press "F1" (Z), and then press "F1" (1-S). Again, since we do not have the original data, we select "F2" (Var) for the data type. Enter the confidence level, population standard deviation, sample mean, sample size. Press "F1" (CALC) to get the interval.

 

We are 95% confident that the average sentence length of the book is in the interval (25.363, 30.236). The 95% confidence interval for the population mean is (25.416, 30.183).