288 Confidence Interval for μ₁ −μ₂, 0² = 0² but Both Unknown Chapter 9 One- and Two-Sample Estimation Problems If ₁ and 2 are the means of independent random samples of sizes n₁ and n2, respectively, from approximately normal populations with unknown but equal variances, a 100(1-a) % confidence interval for ₁-₂ is given by (₁ − 2) — ta/2³p√ + < µ1 − µ₂ < (♬1 − T2) +ta/28p√ + 1 1 n1 n2 1 1 n1 n2 where Sp is the pooled estimate of the population standard deviation and to/2 is the t-value with v = n₁ +n₂ − 2 degrees of freedom, leaving an area of a/2 to the right.

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I am working on a problem with this formula. Does it matter what sample mean is first? I got two vary different answers when I swapped them.

 

FYI just in case, both times a negative number of the answer was on the left, and a positive version of it was on the right, just wanted to say in case this helped. 

288
Confidence
Interval for
μ₁ − μ₂, 0² = 0²/2
-
but Both
Unknown
Chapter 9 One- and Two-Sample Estimation Problems
If ₁ and 2 are the means of independent random samples of sizes n₁ and n2,
respectively, from approximately normal populations with unknown but equal
variances, a 100(1 - a)% confidence interval for µ₁ − μ₂ is given by
1
1
(₁ - ₂) - ta/28p√ + < µ1 − µ2 < (T1 − ☎₂2) +ta/28p√√√7₁ + 2
1 1
n1 n2
n1 n2
where sp is the pooled estimate of the population standard deviation and to/2
is the t-value with v = n₁ + N₂ 2 degrees of freedom, leaving an area of a/2
to the right.
Transcribed Image Text:288 Confidence Interval for μ₁ − μ₂, 0² = 0²/2 - but Both Unknown Chapter 9 One- and Two-Sample Estimation Problems If ₁ and 2 are the means of independent random samples of sizes n₁ and n2, respectively, from approximately normal populations with unknown but equal variances, a 100(1 - a)% confidence interval for µ₁ − μ₂ is given by 1 1 (₁ - ₂) - ta/28p√ + < µ1 − µ2 < (T1 − ☎₂2) +ta/28p√√√7₁ + 2 1 1 n1 n2 n1 n2 where sp is the pooled estimate of the population standard deviation and to/2 is the t-value with v = n₁ + N₂ 2 degrees of freedom, leaving an area of a/2 to the right.
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