The data in the table below presents the hourly quantity of production for three lines of production processes over the first 4 days in XYZ Company. Answer the questions based on the Excel Output given below. Day Process 1 Process 2 Process 3 1 33 33 28 2 30 35 36 3 28 30 30 4 29 38 34 ANOVA: Single Factor SUMMARY Groups Count Sum Average Variance Process 1 4 120 30 4.66667 Process 2 4 136 34 11.3333 Process 3 4 128 32 13.3333 ANOVA Source of Variation SS df MS f P-value Between groups 32 ? ? ? Within groups 88 ? ? Total 120 11 State the null and alternative hypothesis for single factor ANOVA. State the decision rule (α = 0.05). Calculate the test statistic. Make a decision.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The data in the table below presents the hourly quantity of production for three lines of production processes over the first 4 days in XYZ Company. Answer the questions based on the Excel Output given below.
|
Day |
Process 1 |
Process 2 |
Process 3 |
|
1 |
33 |
33 |
28 |
|
2 |
30 |
35 |
36 |
|
3 |
28 |
30 |
30 |
|
4 |
29 |
38 |
34 |
ANOVA: Single Factor
SUMMARY
|
Groups |
Count |
Sum |
Average |
Variance |
|
Process 1 |
4 |
120 |
30 |
4.66667 |
|
Process 2 |
4 |
136 |
34 |
11.3333 |
|
Process 3 |
4 |
128 |
32 |
13.3333 |
ANOVA
|
Source of Variation |
SS |
df |
MS |
f |
P-value |
|
Between groups |
32 |
? |
? |
? |
|
|
Within groups |
88 |
? |
? |
|
|
|
Total |
120 |
11 |
|
|
|
- State the null and alternative hypothesis for single factor ANOVA.
- State the decision rule (α = 0.05).
- Calculate the test statistic.
- Make a decision.
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