Question

the following results for independent random samples taken from two populations. Sample 1 Sample 2 n1-10 n2-30 x1-22.5 x2 20.6 S1-2.5 S2 4.9 a, What is the point estimate of the difference between the two population means (to 1 decimal)? b. What is the degrees of freedom for the t distribution (round down your answer to nearest whole number)? c. At 95% confidence, what is the margin of error (to 1 decimal)? d. What is the 95% confidence interval for the difference between the two population means (to 1 decimal)? Use 2-table. If your answer is negative value, entre minus (-) sign

Answer 1

a.

22.5-20.6 = 1.9

b.

Degrees of freedom = smaller of (n₁ - 1 , n₂ - 1 ) = smaller of (9 , 29) = 9

c.

t_α/2 = 2.26211

MOE = √ (s₁)²/n₁ + (s₂)²/n₂ = √1.4253333333333336 = 1.2

d.

Lower Bound = (x̄₁ - x̄₂) - t_α/2•(√ (s₁)²/n₁ + (s₂)²/n₂ ) = (22.5 - 20.6) - (2.26211)(1.193873248436924) = -0.800672614

Upper Bound = (x̄₁ + x̄₂) + t_α/2•(√ (s₁)²/n₁ + (s₂)²/n₂ ) = (22.5 - 20.6) + (2.26211)(1.193873248436924) = 4.600672614

Confidence Interval = (-0.8, 4.6)