Question

{Exercise 10.01 Algorithmic}

Consider the following results for two independent random samples taken from two populations.

Sample 1	Sample 2
n1 = 50	n2 = 30
x1 = 13.1	x2 = 11.2
σ1 = 2.1	σ2 = 3.2

What is the point estimate of the difference between the two population means?

Provide a 90% confidence interval for the difference between the two population means (to 2 decimals).

Provide a 95% confidence interval for the difference between the two population means (to 2 decimals).

Answer 1

The statistical software output for this problem is:

Two sample Z summary confidence interval:

μ₁ : Mean of population 1 (Std. dev. = 2.1)
μ₂ : Mean of population 2 (Std. dev. = 3.2)
μ₁ - μ₂ : Difference between two means

90% confidence interval results:

Difference	n1	n2	Sample mean	Std. err.	L. limit	U. limit
μ1 - μ2	50	30	1.9	0.65538793	0.82198279	2.9780172

95% confidence interval results:

Difference	n1	n2	Sample mean	Std. err.	L. limit	U. limit
μ1 - μ2	50	30	1.9	0.65538793	0.61546327	3.1845367

Hence,

Point estimate = 1.9

90% confidence interval: (0.82, 2.98)

95% confidence interval: (0.62, 3.18)