Question

Two random samples were selected independently from populations having normal distributions. The statistics given below were extracted from the samples. Complete parts a through c.

x overbar 1 =40.1

x overbar 2=30.5

If σ1=σ2,

s1=33,

and

s2=22,

and the sample sizes are

n 1=10

and

n 2n2equals=1010,

construct a

99%

confidence interval for the difference between the two population means.

The confidence interval is

≤μ1−μ2≤

Answer #1

Given : = 40.1 , = 30.5, s1 = 33 , s2 = 22, n1 = n2 = 10.

In general, (1-)%
confidence interval for μ1−μ2 is obtained as foolow :

where t(/2
, n1+n2-2) = t(0.005, 18) = **2.87844 **(
from the t tables )

and Sp = = 28.04461

Thus, 99% confidence interval for μ1−μ2 is :

( -26.5011955 , 45.7011955 )

Hope this answers your query!

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sample standard deviations is given below:
n1=41, n2=44, x¯1=52.3, x¯2=77.3, s1=6 s2=10.8
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means, assuming equal population variances.
Confidence Interval =

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sample standard deviations is given below:
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Find a 97.5% confidence interval for the difference μ1−μ2μ1−μ2
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Confidence Interval =

Two random samples are selected from two independent
populations. A summary of the samples sizes, sample means, and
sample standard deviations is given below:
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Find a 98% confidence interval for the difference μ1−μ2 of the
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populations. A summary of the samples sizes, sample means, and
sample standard deviations is given below:
n1=45,n2=40,x¯1=50.7,x¯2=71.9,s1=5.4s2=10.6 n 1 =45, x ¯ 1 =50.7, s
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Find a 92.5% confidence interval for the difference μ1−μ2 μ 1 −
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Independent random samples were selected from two quantitative
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6.7
Construct a 95% confidence interval for the difference in the
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Calculate the margin of error. (Round your answer to two decimal
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Two random samples were independently generated from two
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variance of σ². X can be considered the control group and Y the
treatment group.
and
A. Find the likelihood function, i.e., the joint density
function of X and Y.
B. Derive the maximum likelihood estimates of μ1, μ2, and
σ².
C. Suppose the null hypothesis is μ1=μ2 and alternative
hypothesis is μ1 μ2. Write the formula for calculating the
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Construct a? 90% confidence interval for u1 - u2. Two samples
are randomly selected from normal populations. The sample
statistics are given below. Assume that 2?1= 2?2.
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Population
1
2
Sample Size
30
64
Sample Mean
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6.9
Sample Variance
1.37
4.15
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in the population means (μ1 −
μ2). (Round your answers to two decimal
places.)
to

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2. If the number of samples is n1 = 15 and n2 = 15, repeat
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