In a sales pitch TriCon, a strategic security company, claims they have been able to decrease the sales lost to theft in their previous clients by any average of 3%. A sample of quarterly lost sales reports of other companies before and after hiring TriCon is provided below (also available for download here Sales.xlsx). Given σBEFORE = 1.89 and σAFTER = 2.23, at a 1% level of significance can you conclude that, for other companies, hiring TriCon has lead to a reduction in lost sales? YOU CAN ASSUME THE POPULATION TO BE NORMALLY DISTRIBUTED. Quarterly lost sales ($1,000s) Before TriCon Plan After TriCon Plan 4.9 4.43 7.06 4.95 5.75 6.13 6.85 3.14 7.46 3.89
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
In a sales pitch TriCon, a strategic security company, claims they have been able to decrease the sales lost to theft in their previous clients by any average of 3%. A sample of quarterly lost sales reports of other companies before and after hiring TriCon is provided below (also available for download here Sales.xlsx). Given σBEFORE = 1.89 and σAFTER = 2.23, at a 1% level of significance can you conclude that, for other companies, hiring TriCon has lead to a reduction in lost sales? YOU CAN ASSUME THE POPULATION TO BE
| Quarterly lost sales ($1,000s) | |
| Before TriCon Plan | After TriCon Plan |
| 4.9 | 4.43 |
| 7.06 | 4.95 |
| 5.75 | 6.13 |
| 6.85 | 3.14 |
| 7.46 | 3.89 |
| 7.11 | 4.41 |
| 6.13 | 3.38 |
| 4.67 | 4.79 |
| 7.5 | 4.9 |
| 4.52 | 5.91 |
| 5.91 | 3.61 |
| 7.4 | 6.22 |
| 5.43 | 3.74 |
| 4.83 | 5.94 |
| 7.55 | 5.73 |
| 7.11 | 6.73 |
| 7.33 | 4.3 |
| 4.35 | 5.24 |
| 5.38 | 4.07 |
| 6.07 | 6.65 |
| 6.63 | 3.95 |
| 5.85 | |
| 6.88 | |
| 7.3 | |
| 5.36 | |
| 7.83 |
a) Properly state the mathematical hypotheses:
b) p-value:
c) Conclusion:
Step by step
Solved in 4 steps with 3 images
