Question

Two random samples are selected from two independent populations. A summary of the samples sizes, sample means, and sample standard deviations is given below:

n1=51,n2=36,x¯1=56.5,x¯2=75.3,s1=5.3s2=10.7n1=51,x¯1=56.5,s1=5.3n2=36,x¯2=75.3,s2=10.7

Find a 97.5% confidence interval for the difference μ1−μ2μ1−μ2 of the means, assuming equal population variances.

Confidence Interval =

Answer #1

Two random samples are selected from two independent
populations. A summary of the samples sizes, sample means, and
sample standard deviations is given below:
n1=41, n2=44, x¯1=52.3, x¯2=77.3, s1=6 s2=10.8
Find a 96.5% confidence interval for the difference μ1−μ2 of the
means, assuming equal population variances.
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:
n1=39,n2=40,x¯1=50.3,x¯2=73.8,s1=6s2=6.1
Find a 98% confidence interval for the difference μ1−μ2 of the
population means, assuming equal population variances.

Two random samples are selected from two independent
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
1 =5.4 n 2 =40, x ¯ 2 =71.9, s 2 =10.6
Find a 92.5% confidence interval for the difference μ1−μ2 μ 1 −
μ 2 of the means, assuming equal population variances.

Independent random samples were selected from two quantitative
populations, with sample sizes, means, and standard deviations
given below. n1 = n2 = 80, x1 = 125.3, x2 = 123.6, s1 = 5.7, s2 =
6.7
Construct a 95% confidence interval for the difference in the
population means (μ1 − μ2). (Round your answers to two decimal
places.)
Find a point estimate for the difference in the population
means.
Calculate the margin of error. (Round your answer to two decimal
places.)

Two samples are taken with the following sample means, sizes,
and standard deviations
x¯1 = 30 x¯2 = 33
n1 = 48 n2 = 45
s1 = 4 s2 = 3
Estimate the difference in population means using a 88% confidence
level. Use a calculator, and do NOT pool the sample variances.
Round answers to the nearest hundredth.
_____< μ1−μ2 < ______

Two samples are taken with the following sample means, sizes,
and standard deviations
¯x1 = 21 ¯x2 = 29
n1 = 58 n2 = 56
s1 = 4 s2 = 3
Find a 87% confidence interval, round answers to the nearest
hundredth.
< μ1-μ2 <

Independent random samples were selected from populations 1 and
2. The sample sizes, means, and variances are as follows.
Population
1
2
Sample Size
30
64
Sample Mean
11.4
6.9
Sample Variance
1.37
4.15
(a) Find a 95% confidence interval for estimating the difference
in the population means (μ1 −
μ2). (Round your answers to two decimal
places.)
to

1. Two independent samples are taken from two
distinct populations whichproduce sample means, standard deviations
as ̄x1= 104.6, ̄x2= 92.9,s1= 4.8,s2= 6.9,n1= 26,n2= 19.If we use
min(n1−1,n2−1) as the d.f., what t critical value would you usein
constructing a 90% confidence interval
forμ1−μ2?a). 2.101; b) 1.734; c) 1.708; d) 1.645

Independent random samples are selected from two populations.
The summary statistics are given below. Assume unequal variances
for the questions below. m = 5 x ̅ = 12.7 s1 = 3.2
n = 7 y ̅ = 9.9 s2 = 2.1
a) Construct a 95% confidence interval for the difference of the
means.
b) Using alpha = 0.05, test if the means of the two populations
are different based on the result from part (a). Explain your
answer.

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≤

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