A random sample of 144 patients at a local clinic who had cataracts removed during the past year showed an average age of 60 years, with a standard deviation of eight years. A construction of a 95% confidence interval for the population mean is required. What is the standard error of the mean?

Answer 1

To calculate the standard error of the mean (SEM), you can use the following formula:

\[ \text{SEM} = \frac{s}{\sqrt{n}} \]

where:

• \(s\) is the standard deviation of the sample,
• \(n\) is the sample size.

In this case:

• \(s = 8\) years (standard deviation),
• \(n = 144\) (sample size).

Now, plug in the values:

\[ \text{SEM} = \frac{8}{\sqrt{144}} = \frac{8}{12} = \frac{2}{3} \approx 0.67 \text{ years} \]

Thus, the standard error of the mean is approximately 0.67 years.