The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded. Salesperson Before After Sid Mahone $ 320 $ 340 Carol Quick 290 285 Tom Jackson 421 475 Andy Jones 510 510 Jean Sloan 210 210 Jack Walker 402 500 Peg Mancuso 625 631 Anita Loma 560 560 John Cuso 360 365 Carl Utz 431 431 A. S. Kushner 506 525 Fern Lawton 505 619 Hint: For the calculations, assume the "Before" data as the first sample. Click here for the Excel Data File State the decision rule for 0.05 significance level: H0: μd ≥ 0 and H1: μd < 0. (Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.) Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Compute the p-value. (Round your answer to 2 decimal places.) Was there a significant increase in the typical salesperson's weekly income due to the innovative incentive plan? Use the 0.05 significance level.
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 management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded.
| Salesperson | Before | After | ||||||||
| Sid Mahone | $ | 320 | $ | 340 | ||||||
| Carol Quick | 290 | 285 | ||||||||
| Tom Jackson | 421 | 475 | ||||||||
| Andy Jones | 510 | 510 | ||||||||
| Jean Sloan | 210 | 210 | ||||||||
| Jack Walker | 402 | 500 | ||||||||
| Peg Mancuso | 625 | 631 | ||||||||
| Anita Loma | 560 | 560 | ||||||||
| John Cuso | 360 | 365 | ||||||||
| Carl Utz | 431 | 431 | ||||||||
| A. S. Kushner | 506 | 525 | ||||||||
| Fern Lawton | 505 | 619 | ||||||||
Hint: For the calculations, assume the "Before" data as the first sample.
Click here for the Excel Data File
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State the decision rule for 0.05 significance level: H0: μd ≥ 0 and H1: μd < 0. (Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.)
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Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
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Compute the p-value. (Round your answer to 2 decimal places.)
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Was there a significant increase in the typical salesperson's weekly income due to the innovative incentive plan? Use the 0.05 significance level.
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