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a.
Obtain the null and the alternative hypotheses.
a.
Explanation of Solution
The null and alternative hypotheses are given below:
Null Hypothesis
That is, the
Alternative Hypothesis
b.
Give the decision rule.
b.
Explanation of Solution
The treatment and error degrees of freedom are given below:
Treatment degrees of freedom:
Error degrees of freedom:
Here, the level of significance
Step-by-step procedure to obtain the critical F value using Excel-MegaStat:
- In EXCEL, Select Add-Ins > MegaStat > Probability.
- Choose probability> F-distribution> calculate F given probability.
- Enter P as 0.05.
- Enter df1 as 2.
- Enter df2 as 9.
- Click Ok.
Output using the Excel-MegaStat software is given below:
From the output, the critical F value is 4.26.
Decision rule:
If
Therefore, the decision rule is to reject
c.
Find the values of SST, SSE and SS total.
c.
Answer to Problem 11E
The value of SST is 107.20.
The value of SSE is 9.47.
The value of SS total is 116.67.
Explanation of Solution
Here, the level of significance
Step-by-step procedure to obtain the sum of square total, sum of square treatment and sum of square error using Excel-MegaStat:
- Choose MegStat > Analysis of Variance > One-Factor ANOVA.
- Select the column of Treatment 1, Treatment 2 and Treatment 3 in Input
range . - Click OK.
Output using the Excel-MegaStat software is given below:
From the output, the values of SST is 107.20, SSE is 9.47 and SS total is 116.67.
d.
Find an ANOVA table.
d.
Explanation of Solution
From the output in Part (c), the ANOVA table is obtained.
The ANOVA table is given below:
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F |
| Treatments | 107.2 | 2 | 53.6 | 50.96 |
| Error | 9.47 | 9 | 1.05 | |
| Total | 116.67 | 11 |
e.
Find the decision regarding the null hypothesis.
e.
Explanation of Solution
Conclusion:
The F value is 50.96 and the F critical value is 4.26.
Here, F value is greater than F critical value. That is, 50.96 > 4.26.
Using rejection rule, reject the null hypothesis.
Therefore, there is sufficient evidence that at least one mean of all treatment is differ from others.
f.
Check whether there is significant difference between treatment 1 and treatment 2, if null hypothesis is rejected by using the 95% level of confidence.
f.
Explanation of Solution
A 95% confidence interval is as follows:
Where,
From the output in Part (c), the mean of treatment 1 is 9.7, mean of treatment 2 is 2.2, and MSE is 1.052.
Step-by-step procedure to obtain t-critical value using Excel-MegaStat:
- In EXCEL, Select Add-Ins > MegaStat > Probability > t-Distribution.
- Select calculate t given P.
- Enter probability as 0.05.
- Enter df as 9.
- Under Shading, choose two-tail.
- Click Ok.
Output using the Excel-MegaStat software is given below:
From the output, the t is
Therefore, a 95% confidence interval for that difference is 5.8 and 9.2. Here, 0 does not include in the confidence interval.
It means that there is a significant difference between the means of treatment 1 and treatment 2 because the endpoints have same sign or does not include zero.
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Chapter 12 Solutions
STATISTICAL TECHNIQUES FOR BUSINESS AND
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