Final answer:
A 95% confidence interval for the population mean age of Australian males in couples who separated can be calculated by finding the t-multiplier for 123 degrees of freedom and multiplying it by the SEM. Adding and subtracting the margin of error from the sample mean gives a confidence interval of (34.97, 38.33).
Step-by-step explanation:
The question involves constructing a 95% confidence interval for the population mean age of Australian males in couples who separated using the t-distribution. The sample mean is 36.65 years, the standard error of the mean (SEM) is 0.85, and the sample size (n) is 124.
The first step is to find the degrees of freedom (df), which for a t-distribution is the sample size minus one, df = n - 1. In this case, df = 124 - 1 = 123.
Next, we find the t-multiplier for a 95% confidence level and 123 degrees of freedom. Typically, this is found using a t-table or software, but for demonstration, let's assume the t-multiplier is approximately 1.98.
Now, we calculate the margin of error (E) using the formula E = t-multiplier × SEM, which results in E = 1.98 × 0.85 = 1.683.
Finally, we construct the confidence interval by adding and subtracting the margin of error from the sample mean: Lower limit = 36.65 - 1.683 = 34.97 and Upper limit = 36.65 + 1.683 = 38.33.
Thus, the 95% confidence interval is (34.97, 38.33).