According to Holmes et al. (2017), when we have only a single sample, the sample mean is the best estimate of the population mean,. However, we do not expect the sample mean to be equal to the population mean, because there is likely to be some samplingerror. Therefore, in order to make an inference about the population mean, we need some way to describe how well we expect it to be represented by the sample mean.

The most common method for doing this is by way ofconfidence intervals.

A precise calculation shows that if the distribution of sample means is normal with a mean of, then 95% of all sample means lie within 1.96 standard deviations of the population mean; for our purposes in this book, we will approximate this as 2 standard deviations.

Aconfidence intervalis a range of values likely to contain the true value of the population mean.

Two important formula to know.

Margin of error is = E = 1.96s/sqrt(n), where s is the standard deviation of the data and n is the number of items in the data.

Confidence interval formula is from the mean adding and subtracting the margin of error.

Thinking of the many variables tracked by hospitals and doctors' offices, confidence intervals could be created for population parameters (such as means or proportions) that were calculated from many of them. Use weights from 10 boys ages 15-16 (61, 62.5, 64, 64.2, 64.3, 58, 60, 63, 65, 66.2) Discuss the variable and parameter (mean or proportion) you chose, and explain why you would use these to create an interval that captures the true value of the parameter of patients with 95% confidence.

How would changing the confidence interval to 90% or 99% affect the study? Which of these values (90%, 95%, or 99%) would best suit the confidence level according to the type of study chosen? How might the study findings be presented to those in charge in an attempt to affect change at the workplace?