Question

Some groups have clamored that the difference in expected lifespan between males and females is a result of social rather than biological factors. While we cannot determine that, we can examine if any notable difference exists between the average lifespans for men and women, at least in the USA. In a random sample, we found the average lifespan for American women was 80.6, and the average lifespan for American men was 76.5. We want to test the difference in the order Women - Men.

Given DF = 213.6 and standard error = 4.233, what is the value of the test statistic we would use to test for this difference? (3 decimal places)

Answer 1

Solution:

Here we need to use the two sample t test for the difference between the two population means with unequal population variances. For this test, the test statistic formula is given as below:

Test statistic = (X̄₁ - X̄₂)/SE

SE = Standard error

X̄₁ = average lifespan for women = 80.6

X̄₂ = average lifespan for men = 76.5

SE = 4.233

Test statistic = (80.6 - 76.5)/4.233

Test statistic = 0.969