Question
In: Statistics and Probability
Examine the three samples obtained independently from three populations: Population Data Item Group 1 Group 2...
Examine the three samples obtained independently from three populations:
Population Data
| Item | Group 1 | Group 2 | Group 3 |
|---|---|---|---|
| 1 | 14 | 17 | 17 |
| 2 | 13 | 16 | 14 |
| 3 | 12 | 16 | 15 |
| 4 | 15 | 18 | 16 |
| 5 | 16 | 14 | |
| 6 | 16 |
Conduct a one-way analysis of variance on the data assuming the populations have equal variances and the populations are normally distributed. Use alpha = 0.05. Please be sure to clearly state the null and alternative hypotheses, critical value, test statistic, and conclusion.
Solutions
Expert Solution
| Group 1 | Group 2 | Group 3 | Total | |
| Sum | 70 | 67 | 92 | 229 |
| Count | 5 | 4 | 6 | 15 |
| Average, Sum/n | 14 | 16.75 | 15.3333 | |
| Sum of square, Ʃ(xᵢ-x̅)² | 10 | 2.75 | 7.3333 |
Number of treatment, k = 3
Total sample Size, N = 15
df(between) = k-1 = 2
df(within) = N-k = 12
df(total) = N-1 = 14
SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/
N = 16.85
SS(within) = SS1 + SS2 + SS3 =
20.0833
SS(total) = SS(between) + SS(within) =
36.9333
MS(between) = SS(between)/df(between) =
8.425
MS(within) = SS(within)/df(within) =
1.6736
F = MS(between)/MS(within) =
5.0340
p-value = F.DIST.RT(5.0340, 2,12) = 0.0259
Null and Alternative Hypothesis:
Ho: µ1 = µ2 = µ3
H1: at least one mean is different
Test statistic:
F = 5.0340
Critical value:
At α = 0.05, df1 = 2, df2 = 12, critical value, Fc =
3.885
Decision: As F = 5.0340 > Fc =
3.885, Reject the null hypothesis.
orchestra answered 1 year agoRelated Solutions
Examine the three samples obtained independently from three populations: Population Data 3 Item Group 1 Group...
Examine the three samples obtained independently from three
populations:
Population Data 3
Item
Group 1
Group 2
Group 3
1
14
17
17
2
13
16
14
3
12
16
15
4
15
18
16
5
16
14
6
16
Conduct a one-way analysis of variance on the data assuming the
populations have equal variances and the populations are normally
distributed. Use alpha = 0.05.
If warranted, use the Tukey-Kramer procedure to determine which
populations have different means. Use an...
The following three independent random samples are obtained from three normally distributed populations with equal variance....
The following three independent random samples are obtained from
three normally distributed populations with equal variance. The
dependent variable is starting hourly wage, and the groups are the
types of position (internship, co-op, work study).
Group 1: Internship
Group 2: Co-op
Group 3: Work Study
12.5
13
13.5
10.75
12
13.25
12.5
9.5
11.75
12
12.5
13.25
12.5
12.5
12.75
9.5
14
13.5
12.25
14.25
15
Use technology to conduct a one-factor ANOVA to determine if the
group means are...
The following three independent random samples are obtained from three normally distributed populations with equal variances....
The following three independent random samples are obtained from
three normally distributed populations with equal variances. The
dependent variable is starting hourly wage, and the groups are the
types of position (internship, co-op, work study). Round answers to
4 decimal places.
Internship
Co-op
Work Study
9.25
10.5
10.75
9.5
9.75
10
10.75
11
10.5
12
10.75
11.25
10.25
10.25
9.75
10.75
9.25
10.25
10
11.5
9
9.75
9.75
10
10.25
9.5
11.25
12.75
11
10.75
10
11.5
8.75
8.25
10...
The following three independent random samples are obtained from three normally distributed populations with equal variance....
The following three independent random samples are obtained from
three normally distributed populations with equal variance. The
dependent variable is starting hourly wage, and the groups are the
types of position (internship, co-op, work study). We are testing
the claim that the starting salaries for new college graduate are
different depending on the positions at α=0.2α=0.2 given the
following data
Group 1: Internship
Group 2: Co-op
Group 3: Work Study
10
11.25
16
14.75
13
14
10.5
13.5
14
9.5...
The following three independent random samples are obtained from three normally distributed populations with equal variances....
The following three independent random samples are obtained from
three normally distributed populations with equal variances. The
dependent variable is starting hourly wage, and the groups are the
types of position (internship, co-op, work study). Round answers to
4 decimal places.
Internship
Co-op
Work Study
11.25
11
10.5
12.5
11.75
14.75
10.75
14
10.5
11.5
9.5
9.5
12.5
13.5
11
11.75
10.75
13.25
11.75
14.25
10.5
14.25
10.75
12.5
12.5
12.75
12.25
11.5
11.25
9.5
12
12.25
11.75
10.5
12...
The following three independent random samples are obtained from three normally distributed populations with equal variance....
The following three independent random samples are obtained from
three normally distributed populations with equal variance. The
dependent variable is starting hourly wage, and the groups are the
types of position (internship, co-op, work study).
Group 1: Internship
Group 2: Co-op
Group 3: Work Study
9
9
13.75
9.25
12.75
11.75
12
11.5
11.25
11.75
14.75
16.25
12.25
8.75
10
11.75
10.5
11.5
10
9.75
12.75
11.25
10.75
15.5
Do not forget to convert this table from parallel format
(i.e.,...
The following three independent random samples are obtained from three normally distributed populations with equal variance....
The following three independent random samples are obtained from
three normally distributed populations with equal variance. The
dependent variable is starting hourly wage, and the groups are the
types of position (internship, co-op, work study).
Group 1: Internship
Group 2: Co-op
Group 3: Work Study
15
14.75
14.25
17.25
9.75
15.5
13
15.25
16.25
16.75
14
13.5
13
14.25
13.75
13
16
15.75
15.25
9.5
15.25
17.5
12
16.75
Do not forget to convert this table from parallel format
(i.e.,...
1. If two samples are drawn independently from the same population, then the sample means will...
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true or false?
2. If two samples are drawn independently from the same
population, then their sample standard deviations will be the
same.
true or false?
3. You can find below the results from Tukey's Honestly
Significant Difference procedure with familywise significance level
0.05 for the agricultural experiment above. Which of the following
can be concluded at this level?
diff
lwr...
The following information is obtained from two independent samples selected from two populations. n 1 =...
The following information is obtained from two independent
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interval for μ 1 - μ 2 . Round your answers to two decimal
places.
The difference between the two population means is :
5. (36 pts) Suppose three samples are selected from three populations as follows: Sample 1: 2,...
5. (36 pts) Suppose three samples are selected from three
populations as follows: Sample 1: 2, 6 Sample 2: 6, 8, 10 Sample 3:
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whether there is evidence of a difference in the population
means.
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