Question

The accompanying table shows two samples that were collected as matched pairs. Complete parts (a) through (d) below.

Pair:

1 7 5

2 5 2

3 8 7

4 4 5

5 5 1

6 9 9

a. State the null and alternative hypotheses to test if the populatio represented by Sample 1 has a higher mean than the population represented by Sample 2. Let ud be the population mean of matched-pair differences for Sample 1 minus Sample 2. Choose the correct answer below.

b. Calculate the appropriate test statistic and interpret the results of the hypothesis test using a=0.05.

c. Identify the p-value and interpret the result.

d. What assumptions need to be made in order to perform this procedure?

Answer #1

a)

H0 : mud = 0

HA: mud not=0

b)

Before after dbar

7 5 2

5 2 3

8 7 1

4 5 -1

5 1 4

9 9 0

dbar = μ(before) - μ(after) = 1.5

s(dbar) = 1.8708

SE = s(dbar)/sqrt(n)

= 1.8708/sqrt(6)

= 0.7638

Test Statisitcs,

t = dbar/SE

= 1.5/0.7638

= 1.9640

c)

p value= 0.1067

Fail to reject H0 as p value > 0.05 significance level

d)

The sample of paired differences must be reasonably random.

The paired differences d = x1 - x2 should be approximately
normally distributed or be a large

sample (need to check n ≥ 30 ). This procedure is robust if there
are no outliers and little skewness in the paired differences.

The following two samples were collected as matched pairs.
Complete parts? (a) through? (d) below. Pair 1 2 3 4 5 6 7 Sample 1
4 5 8 5 7 6 7 Sample 2 5 3 4 3 4 5 4 a. State the null and
alternative hypotheses to test if a difference in means exists
between the populations represented by Samples 1 and 2. Let mud be
the population mean of? matched-pair differences for Sample 1 minus
Sample 2....

The accompanying table contains two samples that were collected
as matched pairs. Complete parts a and b below.
Pair
Sample 1
Sample 2
1
10
4
2
6
7
3
4
6
4
8
3
5
11
5
6
7
9
7
8
5
8
7
5
A.
Construct a 90?% confidence interval to estimate difference in
means between the populations from which Sample 1 and 2 were
drawn.
UCL d-overbar
= ??
LCL d-overbar
= ??
B . What...

The following two samples were collected as matched pairs: Pair
1 2 3 4 5 6 7 8 Sample 1 8 4 6 9 9 7 9 8 Sample 2 5 7 6 5 6 9 7 6
a. State the null and alternative hypotheses to estimate the
difference in means between the populations from which Samples 1
and 2 were drawn. b. Calculate the appropriate test statistic and
interpret the results of the hypothesis test using α = 0.1....

Now suppose a larger sample (30 pairs vs 10 pairs) was
collected and a paired t test was used to analyze the data. The
output is shown below.
Paired Samples
Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
Female salaries
6773.33
30
782.099
142.791
Male salaries
7213.33
30
875.227
159.794
Paired Samples
Correlations
N
Correlation
Sig.
Pair 1
Female salaries &
Male salaries
30
.881
.000
Paired Samples
Test
Paired Differences
t
df
Sig. (2-tailed)
Mean
Std. Deviation...

The accompanying table contains the service ratings of 14
different Internet and TV providers. Complete parts (a)
through(d) below
At the 0.01 level of significance, is there evidence of a
difference in the mean service rating between TV and
Internetservices?Let mu 1be the mean TV service rating and let mu
2 be the mean Internet service rating. State the null and
alternative hypotheses. Choose the correct answer below.
b.Determine the T Test and critical values
c. Determine the P value...

QUESTION 1
The samples are necessarily considered a dependent when
a.
repeated measures are made on the same subjects
b.
both groups consist of males
c.
both groups consist of 8th grade pupils
d.
any of the above is true
QUESTION 2
Observations are dependent when
a.
the same subjects have been used for both sets of
observations
b.
subjects have been matched on some variable related to the
varialbe observed
c.
either of the above is true
d.
the...

Refer to the data set in the
accompanying table. Assume that the paired sample data is a simple
random sample and the differences have a distribution that is
approximately normal. Use a significance level of
0.01
to test for a
difference between the weights of discarded
paper?
(in
pounds) and
weights of discarded plastic?
(in
pounds).
Household Paper Plastic 1 9.83 6.26 2 8.72 9.20 3 6.16
5.88 4 14.33 6.43 5 13.61 8.95 6 9.41 3.36 7 15.09 9.11...

10-10. The following table contains information on matched
sample values whose differences are normally distributed.
(You may find it useful to reference the appropriate
table: z table or t
table)
Number
Sample 1
Sample 2
1
18
22
2
13
11
3
22
23
4
23
20
5
17
21
6
14
16
7
18
18
8
19
20
a. Construct the 99% confidence interval for the mean
difference μD. (Negative values should
be indicated by a minus sign. Round...

Use a t-distribution and the given matched pair sample
results to complete the test of the given hypotheses. Assume the
results come from random samples, and if the sample sizes are
small, assume the underlying distribution of the differences is
relatively normal. Assume that differences are computed using
d=x1-x2.
Test H0 : μd=0 vs Ha : μd>0 using the paired data in the
following table:
Situation 1
120
156
145
175
153
148
180
135
168
157
Situation 2
120...

Assume that the differences are normally distributed. Complete
parts (a) through (d) below.
Observation
1
2
3
4
5
6
7
8
Upper X Subscript iXi
43.2
43.4
44.0
42.342.3
50.4
43.4
52.5
49.6
Upper Y Subscript iYi
45.8
45.1
47.8
46.1
49.8
46.1
52.9
48.8
(a) Determine
d Subscript i Baseline equals Upper X Subscript i Baseline minus
Upper Y Subscript idi=Xi−Yi
for each pair of data.
Observation
1
2
3
4
5
6
7
8
di
(Type integers...

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