Question

A study was conducted to determine if the salaries of librarians from two neighboring cities were equal. A sample of 15 librarians from each city was randomly selected. The mean from the first city was $28,900 with a standard deviation of $2300. The mean from the second city was $30,300 with a standard deviation of $2100. Construct a 95% confidence interval for u1 - u2.

A) (-2871, 567) B) (-2054,238 C) (-3125, 325) D) (-4081, 597)

Answer 1

Calculation

Pooled Variance
s²_p = ((df₁)(s²₁) + (df₂)(s²₂)) / (df₁ + df₂) = 135800000 / 28 = 4850000

Standard Error
s_{(M1 - M2)} = ?((s²_p/n₁) + (s²_p/n₂)) = ?((4850000/15) + (4850000/15)) = 804.16

Confidence Interval
_u1 - u₂ = (M₁ - M₂) ± ts_{(M1 - M2)} = -1400 ± (2.05 * 804.16) = -1400 ± 1647.24

95% CI [247.24, -3047.24].

You can be 95% confident that the difference between your two population means (u₁ - u₂) lies between -3047.24 and 247.24  

i.e.C)(-3125, 325)