Following is the data related to the daily production of the two factories of same product located in two different states. Factory Daily Production Factory 1 66 66 73 83 74 73 73 69 82 71 73 66 67 80 79 78 Factory 2 66 63 71 65 65 67 57 48 71 73 68 58 62 81 60 62 72 72 57 77 68 Calculate the following [2] Daily Production of Factory 1 Daily Production of Factory 1 Sample Size Degree of freedom Mean Variance Standard Deviation Calculate the ratio of two variances and test the equality of the variances and comments.[1] Calculate the value of pool standard deviation (Sp), degree of freedom in the light of part “b” and SED [1] Write the null and alternative hypothesis for comparing the production of two factories. [1]
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.
Following is the data related to the daily production of the two factories of same product located in two different states.
|
Factory |
Daily Production |
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|
Factory 1 |
66 |
66 |
73 |
83 |
74 |
73 |
73 |
69 |
82 |
71 |
73 |
66 |
67 |
80 |
79 |
78 |
|
|
|
|
|
|
Factory 2 |
66 |
63 |
71 |
65 |
65 |
67 |
57 |
48 |
71 |
73 |
68 |
58 |
62 |
81 |
60 |
62 |
72 |
72 |
57 |
77 |
68 |
- Calculate the following [2]
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Daily Production of Factory 1 |
Daily Production of Factory 1 |
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|
|
|
|
Degree of freedom |
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|
Mean |
|
|
|
Variance |
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|
Standard Deviation |
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- Calculate the ratio of two variances and test the equality of the variances and comments.[1]
- Calculate the value of pool standard deviation (Sp), degree of freedom in the light of part “b” and SED [1]
- Write the null and alternative hypothesis for comparing the production of two factories. [1]
- Calculate the critical values “ttab”, and tcal [1]
- Write the conclusion for the null hypothesis of part “d” [1]
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