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# One way & Two way ANOVA

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1. Two aptitude tests are currently being used to screen applicants for a certain position within a company. The question arose as to whether the two tests are comparable, i.e., whether they yield the same results. Six applicants were selected at random to take both tests (in a random order). The following scores were recorded:

Applicant Test A Test B
1 85 87
2 93 94
3 98 92
4 68 73
5 76 73
6 83 85

a. What statistical test do you use in order to determine whether there is a difference in scores between the two aptitude tests?

b. Complete the table
Applicant Test A Test B Difference Rank
1 85 87
2 93 94
3 98 92
4 68 73
5 76 73
6 83 85

c. Compute the values for the test statistic. Use = 0.10.

d. State the rejection rule

e. Conclude about the differences in th tests scores.

2. A mechanical engineer at a manufacturing plant keeps a close watch on the performance and condition of the machines. The following data are the weight losses (in milligrams) of certain machine parts due to friction when used with three different lubricants.

Lubricant A Lubricant B Lubricant C
12 10 12
9 8 8
8 9 14
11 13 11
10 8 12
8 7 13
7 5 7
6 11 8

a. State the null and alternative hypotheses to test whether there is a significant difference in mean weight losses among the three lubricants.
b. How many degrees of freedom are associated with the F test statistic?
e. Set up the rejection decision rule for = 0.01.
f. What is the appropriate conclusion?

3. Ann May wishes to determine if the mean price of grocery items is the same for five supermarkets in her city. The same seven food (and brand) items were priced at the five stores.

a. Complete the partial ANOVA table below for testing the null hypothesis of no difference in the true mean price for the five stores in a completely randomized design. Can you reject the null hypothesis? Use = 0.05.

Source DF SS MS F
Store * * * *
Error * 249.1301 8.3043
Total * 252.0784

b. Complete the ANOVA table below where the grocery items were treated as blocks. Can you reject the null hypothesis of no difference between the true mean price for the five stores? Use &#61537; = 0.05.

Source DF SS MS F
Store * 2.9483 * *
Item * 247.3979 * *
Error * * *
Total * 252.0784

c. Why is it important to treat the food items as blocks? Compare parts (a) and (b).

4. Due to his high blood pressure, Sam watches the sodium content of the foods that he eats. Five samples for each of four brands of canned turkey (97% fat free) were tested for sodium content, measured in milligrams of sodium per 2-ounce serving.

Brand 1 Brand 2 Brand 3 Brand 4
250 175 175 200
251 185 180 210
260 175 180 210
255 180 170 195
245 165 190 205

The following summary table and ANOVA were generated by statistical software as shown below:
ANOVA TABLE
Source of Variation df SS MS F P-value F crit
Brand 3 18632.4 6210.8 134.871 0.000 3.23887
Error 16 736.8 46.05

Total 19 19369.2

a. State the hypotheses and use the p-value approach to conclude concerning mean amount of sodium in the four brands. Let = 0.05.

b. Using the following output generated by Minitab determine which of the means are different.

Tukey's pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.0113
Critical value = 4.05
Intervals for (column level mean) - (row level mean)

1 2 3
2 63.91
88.49
3 60.91 -15.29
85.49 9.29
4 35.91 -40.29 -37.29
60.49 -15.71 -12.71

See attached file for problems.

https://brainmass.com/statistics/analysis-of-variance/one-way-two-way-anova-317895

#### Solution Summary

The solution provides step by step method for the calculation of Mean Square and common population variance from one-way ANOVA. The solution also provides step by step method for the completion of a partial ANOVA table. Formula for the calculation and Interpretations of the results are also included.

\$2.19

## Anova Function in Excel to test Hypotheses

I need assistance testing these hypotheses using Anova (Single Factor) in Excel. I need to show what is returned( F-statistic, F critical, and a P-value.) I then need to use these values to reject or accept H0.

I have done this in Excel, but need help making sure my figures are right and determining if I accept or reject HO. Please return a help on making sure these are right and determining if i accept or reject the hypothesis.

My first claim is :

There is no difference between the level of intrinsic job satisfaction for employees in the Human Resource Department than in the Information Technology Department.

The Null hypothesis will be: H0: m1 = m2

Where m1 = mean of response to question 2 for those who fall under category 1 for question 1.
Where m2 = mean of response to question 2 for those who fall under category 2 for question 1.

The alternate hypothesis will be: H1: m1 does not equal m2

My work:
Anova: Single Factor

SUMMARY
Groups Count Sum Average Variance
Column 1(Department) 111 211 1.900901 0.09009
Column 2 (Intrinsic Job Satisfaction) 111 559.51 5.040631 1.244655

ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 547.1136 1 547.1136 819.8024 3.83E-76 3.884074
Within Groups 146.822 220 0.667373

Total 693.9356 221

The second claim is:

I claim that employees in the Administration Dept are Extrinsically more satisfied than other employees in other departments.

The Null hypothesis will be: H0: m1 = m2

Where m1 = mean of response to claim for those who fall under Administrative department
Where m2 = mean of response to question 2 for those who fall under other departments

The alternate hypothesis will be: H1: m1 > m2

My work:

Anova: Single Factor

SUMMARY
Groups Count Sum Average Variance
Column 1 177 531 3 0
Column 2 177 902.2 5.097175 2.593003

ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 389.2357 1 389.2357 300.22 4.5E-49 3.868012
Within Groups 456.3686 352 1.296502

Total 845.6043 353

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