Question

A sociologist expects the life expectancy of people in Africa is different than the life 31) expectancy of people in Asia. The data obtained is shown in the table below. Determine the 95% confidence interval for the difference in the population means. Africa X 1 = 55.3 yr. σ1 = 8.1 yr. n1 = 53 Asia X 2 = 65.2 yr. σ2 = 9.3 yr. n2 = 42

Answer 1

The 95% confidence interval for the difference in population means is (5.635,11.965) years.

In statistical hypothesis testing, particularly when comparing the means of two populations, confidence intervals provide a range within which we can reasonably expect the true parameter (in this case, the difference in population means) to lie. The formula for constructing a confidence interval for the difference in means involves incorporating sample means, sample standard deviations, and sample sizes for the two populations, as well as the Z-score corresponding to the desired level of confidence.

For this scenario, where we are comparing the life expectancy of people in Africa and Asia, we follow a standard procedure. The sample means (X1 =55.3 and X​2=65.2), sample standard deviations (s1=8.1 and s2​=9.3), and sample sizes (n1​=53 and n​2 =42) are used in the formula along with the Z-score for a 95% confidence interval (Z≈1.96).

The resulting 95% confidence interval (5.635,11.965) years implies that we are 95% confident that the true difference in life expectancy between Africa and Asia falls within this range. In other words, if we were to repeat this sampling procedure numerous times and construct confidence intervals, we would expect about 95% of them to contain the true difference in life expectancy.