Get your paper written from scratch within the tight deadline. Our service is a reliable solution to all your troubles. Place an order on any task and we will take care of it. You won’t have to worry about the quality and deadlines
Independent random samples of 64 observations
each are chosen from two normal populations with the following means and
standard deviations:
Population
1
Population
2
µ1 = 12
µ2 = 10
Ϭ1 = 4
Ϭ2 = 3
Let 1
and 2
denote the two sample means.
Give the mean and standard deviation of the
sampling distribution of 1.
Give the mean and standard deviation of the
sampling distribution of 2.
Suppose you were to calculate the
difference (1
– 2)
between the sample means. Find the mean
and standard deviation of the sampling distribution of (1
– 2).
Will the statistic (1
– 2)
be normally distributed? Explain.
In order to compare the means of two
populations, independent random samples of 400 observations are selected from
each population, with the following results:
Sample
1
Sample
2
1=
5,275
2
= 5,240
s1 = 150
s2 = 200
Use a 95% confidence interval to estimate the
difference between the population means (µ1 – µ2). Interpret the confidence interval.
Test the null hypothesis H0: (µ1 – µ2) = 0 versus the
alternative hypothesis Ha: (µ1
– µ2) ≠ 0. Give the
significance level of the test, and interpret the result.
Suppose the test in part b was conducted with
the alternative hypothesis Ha:
(µ1 – µ2) > 0. How would your answer to part b
change?
Test the null hypothesis H0: (µ1 – µ2) = 25 versus the
alternative hypothesis Ha: (µ1
– µ2) ≠ 25. Give the
significance level and interpret the result.
Compare your answer to the test conducted in part b.
What assumptions are necessary to ensure the
validity of the inferential procedures applied in parts a – d?.
Assume that Ϭ12 = Ϭ22
= Ϭ2. Calculate the pooled
estimator of Ϭ2 for each of the following cases:
s12 = 120, s22
= 100, n1 = n2
= 25
s12 = 12, s22
= 20, n1 =20, n2
= 10
s12 = 0.15, s22
= 0.20, n1 =6, n2
= 10
s12 = 3,000, s22
=2,500, n1 =16, n2
= 17
Note that the pooled estimate is a weighted
average of the sample variances. To
which of the variances does the pooled estimate fall nearer in each of the
above cases?
Suppose you manage a plant that purifies its
liquid waste and discharges the water into a local river. An EPA inspector has collected water
specimens of the discharge of your plant and also water specimens in the river
upstream from your plant. Each water
specimen is divided into five parts, the bacteria count is read on each, and
the mean count for each specimen is reported.
The average bacteria count for each of six specimens are reported in the
following table for the two locations.
Plant
Discharge
Upstream
30.1
36.2
33.4
29.7
30.3
26.4
28.2
29.8
34.9
27.3
31.7
32.3
Why might the bacteria counts shown here tend to
be approximately normally distributed?
What are the appropriate null and alternative
hypotheses to test whether the mean bacteria count for the plant discharge
exceeds that for the upstream location? Be sure to define any symbols you use.
What assumptions are necessary to ensure the
validity of this test?
A paired difference experiment produced the
following data:
nD = 18 1 =
92 2 =
95.5 D
= -3.5 sD2
= 21
Determine the values of t for which the null hypothesis, µ1 – µ2 = 0,
would be rejected in favor of the alternative hypotheses, µ1 – µ2
< 0. Use α = .10.
Conduct the paired difference test described in
part a. Draw the appropriate
conclusions.
What assumptions are necessary so that the paired
difference test will be valid?
Find a 90% confidence interval for the mean
difference µD.
Which of the two inferential procedures, the
confidence interval of part d of the test of hypothesis of part b, provides
more information about the differences between the population means?
Facility layout and material flow path design
are major factors in the productivity analysis of automated manufacturing
systems. Facility layout is concerned
with the location arrangement o machines and buffers for work-in-process. Flow path design is concerned with the
location arrangement of machines and buffers for work -in-process. Flow path design is concerned with the
direction of manufacturing material flows (e.g., unidirectional or
bidirectional). A manufacturer of
printed circuit boards (PCBs) is interested in evaluating two alternative
existing layout and flow path designs.
The output of each design was monitored for eight consecutive working
days.
Working Days
Design
1
Design
2
8/16
1,220 units
1,273 units
8/17
1,092 units
1,363 units
8/18
1,136 units
1.342 units
8/19
1,205 units
1,471 units
8/20
1,086 units
1,299 units
8/23
1,274 units
1,457 units
8/24
1,145 units
1,263 units
8/25
1,281 units
1,368 units
Construct a 95% confidence interval for the
difference in mean daily output of the two designs.
What assumptions must hold to ensure the validity
of the confidence interval?
Design 2 appears to be superior to Design
1. Is this confirmed by the confidence
interval?
Construct a 95% confidence interval for (p1
– p2) in each of the following situations:
n1 = 400, = 0.65; n2=
400, = 0.58
n1 = 180, = 0.31; n2=
250, = 0.25
n1 = 100, = 0.46; n2=
120, = 0.61
Suppose you want to estimate the difference
between two population means correct to within 1.8 with a 95% confidence
interval. If prior information suggests that
the population variances are approximately equal to Ϭ12 =
Ϭ22 = 14 and you want to select independent random
samples of equal size from the population, how large should the sample sizes, n1 and n2be?
Determine each of the following F values:
F.05
where v1-= 9
and v2= 6
F.01
where v1-= 18
and v2= 14
F.025
where v1-= 11
and v2= 4
F.10
where v1-= 20
and v2= 5
When new instruments are developed to perform
chemical analyses of products (food, medicine etc.), they are usually evaluated
with respect to two criteria: accuracy and precision. Accuracy
refers to the ability of an instrument to identify correctly the nature and
amounts of a product’s components. Precision refers to the consistency with
which the instrument will identify the components of the same material. Thus, a large variability in the
identification of a single batch of a product indicates a lack of
precision. Suppose a pharmaceutical firm
is considering two brands of an instrument designed to identify the components
of certain drugs. As part of a
comparison of precision, 10 test-tube samples of a well-mixed batch of a drug
are selected and then five are analyzed by instrument A and five by instrument
B. The data shown below are the
percentages of the primary component of the drug given by the instruments. Do these data provide evidence of a
difference in the precision of the two machines? Use α = 0.10.
