Question
In: Statistics and Probability
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 alpha level of 0.05.
Solutions
Expert Solution
A single factor ANOVA is used in excel to test the null hypothesis that all the means are equal. The hypothesis is defined as,
Null Hypothesis: At least one mean differ significantly.
Alternative Hypothesis: All the means are
equal, 
The test is performed in excel by using following steps,
Step 1: Write the data values in excel. The screenshot is shown below,
Step 2: DATA > Data Analysis > ANOVA: single Factor > OK. The screenshot is shown below,
Step 3: Select Input Range: All the data values column, Alpha = 0.05. The screenshot is shown below,
The result is obtained. The ANOVA table is shown below,
From the ANOVA result summary,
Since the P-value is less than 0.05 at 5% significance level, the null hypothesis is rejected. Hence we can conclude that there is atleast one mean is significantly differ.
Post-Hoc test
Now, the Tukey-Kramer (T-K) multiple comparisons procedure is used to test all the pairwise comparison and identify which pair is significantly different.
The Tukey-Kramer method uses the formula,
The q value is obtained using the Studentized Range q table for significance level = 0.05, number of groups, k = 3, degree of freedom = N - k = 15 - 3 = 12.
The HSD value for group 1 and 2 comparison ,
The HSD value for group 1 and 3 comparison ,
The HSD value for group 2 and 3 comparison ,
Now,
The mean value for each groups are,
| Groups | Average |
| Group 1 | 14 |
| Group 2 | 16.75 |
| Group 3 | 15.33333 |
There are 3 possible comparison as follows,
| Comparison | Difference | HSD | ||
 |
2.75 | > | 2.3153 | Significant |
 |
1.333333 | < | 2.0899 | Not Significant |
 |
1.416667 | < | 2.2279 | Not Significant |
The mean difference in Group 1 vs Group 2 is significant.
orchestra answered 2 years agoRelated Solutions
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...
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...
1. If two samples are drawn independently from the same
population, then the sample means will be the same.
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
samples selected from two populations. n 1 = 250 x ¯ 1 = 5.72 σ 1 =
2.78 n 2 = 290 x ¯ 2 = 4.43 σ 2 = 1.21 Construct a 98 % confidence
interval for μ 1 - μ 2 . Round your answers to two decimal
places.
The difference between the two population means is :
You obtain three samples from three different populations. Observed genotype frequencies. Population 1 AA=0.70 ; Aa=0.25...
You obtain three samples from three different populations.
Observed genotype frequencies.
Population 1 AA=0.70 ; Aa=0.25 ; aa = 0.05
Population 2 AA=0.35 ; Aa=0.55 ; aa=0.10
Population 3 AA=0.45 ; Aa=0.40 ; aa=0.15
Populations 2 and 3 have no barrier between them. But
populations 1 and 2, and populations 1 and 3 have a barrier between
them.
What are the FST values between these three pairs of
populations?
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