Question

We selected a random sample of 100 StatCrunchU students, 67 females and 33 males, and analyzed their responses to the question, "What is the total amount (in dollars) of credit card debt you have accrued to date?"

With more than 30 in each random and independent sample, conditions are met for modeling the distribution of differences in sample means using a T-model. Therefore, we will proceed with finding a confidence interval to estimate the gender difference in credit card debt for StatCrunchU students.

Summary statistics for CC Debt:
Group by: Gender

Gender	Mean	Std. dev.	n
Female	2577.75	1916.29	67
Male	3809.42	2379.47	33

Use StatCrunch to find the 95% confidence interval estimating the difference µ1 – µ2, where µ1 is the mean credit card debt for all female StatCrunchU students and µ2 is the mean credit card debt for all male StatCrunchU students.

Since the numbers are dollars, round to two decimal places when you enter your answer.

What is the lower limit on the confidence interval?

What is the upper limit on the confidence interval?

Answer 1

Pooled Variance
s²_p = ((df₁)(s²₁) + (df₂)(s²₂)) / (df₁ + df₂) = 423543125.42 / 98 = 4321868.63
Standard Error
s_{(M1 - M2)} = √((s²_p/n₁) + (s²_p/n₂)) = √((4321868.63/67) + (4321868.63/33)) = 442.12

Confidence Interval
μ₁ - μ₂ = (M₁ - M₂) ± ts_{(M1 - M2)} = 1231.67 ± (1.98 * 442.12) = 1231.67 ± 877.3753

You can be 95% confident that the difference between your two population means (μ₁ - μ₂) lies between 354.2947 and 2109.0453.

lower limit on the confidence interval:354.2947

upper limit on the confidence interval:2109.0453.