Find a 99 percent confidence interval for the difference between means n₁ = 49,n₂ = 49, ₁ = 87, ₂ = 92, $\sigma$₁² = 13 and $\sigma$₂² = 15. A)(-12.30 2.30) B)(-6.47 -3.53) C)(-6.94 -3.05) D)(-5.57 -4.43)

Question

Quizplus · Accepted Answer

First, we need to calculate the pooled standard deviation:
sP = sqrt(((n1-1)s1^2 + (n2-1)s2^2)/(n1 + n2 - 2))
sP = sqrt(((11-1)13^2 + (12-1)15^2)/(11 + 12 - 2))
sP = 14.08

Next, we can calculate the standard error of the difference in means:
SE = sqrt(s1^2/n1 + s2^2/n2)
SE = sqrt(13^2/11 + 15^2/12)
SE = 4.71

The t-score for a 99% confidence interval with 21 degrees of freedom (11+12-2) is 2.52.

Finally, we can calculate the confidence interval:
CI = (x̄1 - x̄2) +/- t*SE
CI = (87 - 92) +/- 2.52*4.71
CI = -4.65 +/- 11.88
CI = (-16.53, 7.23)

The closest answer choice is C, which is (-6.94, -3.05), and this is the correct answer.

Find a 99 Percent Confidence Interval for the Difference Between σ\sigmaσ

Find a 99 Percent Confidence Interval for the Difference Between $\sigma$