Two samples are taken with the following sample means, sizes, and standard deviations¯x1x¯1 = 40 ¯x2x¯2 = 34n1n1 = 58 n2n2 = 54s1s1 = 4 s2s2 = 2 Two samples are taken with the following sample means, sizes, andstandard deviations71 = 40 2 = 34n = 58 n2 = 5481 = 4 82 = 2%3D%3!Estimate the difference in population means using a 85% confidencelevel. Use a calculator, and do NOT pool the sample variances.Round answers to the nearest hundredth.< l1 - 42 <

Name: Two samples are taken with the following sample means, sizes, and stan
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Description: Two samples are taken with the following sample means, sizes, and standard deviations¯x1x¯1 = 40 ¯x2x¯2 = 34n1n1 = 58 n2n2 = 54s1s1 = 4 s2s2 = 2 Two samples are taken with the following sample means, sizes, andstandard deviations71 = 40 2 = 34n = 58

Givenx¯1=40n1=58s1=4x¯2=34n2=54s2=2 α=significance level=0.15

Answered: Two samples are taken with the…

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Two samples are taken with the following sample means, sizes, and standard deviations
¯x1x¯1 = 40 ¯x2x¯2 = 34
n1n1 = 58 n2n2 = 54
s1s1 = 4 s2s2 = 2

Two samples are taken with the following sample means, sizes, and
standard deviations
71 = 40 2 = 34
n = 58 n2 = 54
81 = 4 82 = 2
%3D
%3!
Estimate the difference in population means using a 85% confidence
level. Use a calculator, and do NOT pool the sample variances.
Round answers to the nearest hundredth.
< l1 - 42 <

Expert Solution

Step 1

$G i v e n {\bar{x}}_{1} = 40 n_{1} = 58 s_{1} = 4 {\bar{x}}_{2} = 34 n_{2} = 54 s_{2} = 2$

$α = s i g n i f i c a n c e l e v e l = 0.15$

Step 2

$T h e c o n f i d e n c e i n t e r v a l f o r d i f f e r e n c e o f t w o p o p u l a t i o n m e a n s (μ_{1} - μ_{2}) i s : ({\bar{x}}_{1} - {\bar{x}}_{2}) \pm t \times \sqrt{(\frac{{s_{1}}^{2}}{n_{1}} + \frac{{s_{2}}^{2}}{n_{2}})} w h e r e t = c r i t i c a l v a l u e c o r r e s p o n d s t o t h e c o n f i d e n c e l e v e l a n d d f = s m a l l e r (n_{1} - 1, n_{2} - 1)$

$D e g r e e o f f r e e d o m : d f = s m a l l e r (58 - 1, 54 - 1) d f = s m a l l e r (57, 53) d f = 53 T h e c r i t i c a l v a l u e i s : t = 1.4607 (b y u \sin g c r i t i c a l v a l u e c a l c u l a t o r)$

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