A Company Offered Half Of Its Employees A Bonus

A Company Offered One Half Of Its Employees A Bonus If The Production

A company offered one half of its employees a bonus if the production of cookies increased by 15%. The other half of the employees was not offered a bonus. As the end of the month, production in the group that did not get the bonus offer increased by a mean of 20, and production in the bonus group increased by a mean of 10. What is the correct order of steps to determine if the results are significant? A: Calculate the probability of a difference of 10. B: Calculate the difference of the means. C: Randomly separate the employees’ individual results into two groups. D: Calculate the mean of each group. E: Run the experiment many times.

Paper For Above instruction

The question involves determining whether the observed difference in production increase between two employee groups—those offered a bonus versus those not offered—is statistically significant. To approach this, a systematic sequence of statistical steps should be followed, ensuring rigorous testing of the hypothesis that the bonus had a measurable effect on production increases. The appropriate sequence begins with data organization, followed by statistical calculations, randomization methods, and hypothesis testing procedures.

The first step in evaluating the significance of the difference in production increases is to organize the data into two groups: employees who received the bonus and those who did not. Since individual employee results are not explicitly given, but group means are, the process involves understanding the distribution of individual results within each group. Because the experiment was designed to compare these two groups, the first procedural step should be to randomly separate individual employee results into these two groups if the data are not already grouped. This process mimics the random assignment of employees to experimental conditions and creates a framework suitable for further statistical analysis. This step corresponds to option C: "Randomly separate the employees’ individual results into two groups."

Once the data are organized, the next essential step is to compute the mean production increase for each group to formalize the basis of comparison. Calculating these means allows researchers to quantify the observed difference in production, which has already been observed as a 10-unit difference (20 in the non-bonus group minus 10 in the bonus group). While this step is theoretically already provided, the procedure involves executing the calculation, aligning with option D: "Calculate the mean of each group." This ensures clarity on the central tendency of each group's results.

Following the calculation of the means, the next logical step is to determine the difference between these means. Such a difference quantifies the observed effect, which in this case appears as a 10-unit discrepancy. This step is explicitly step B: "Calculate the difference of the means." Calculating the difference sets the stage for the statistical inference about whether this observed difference is likely due to chance or reflects a true effect caused by the bonus.

The subsequent crucial phase involves assessing the probability that such a difference could occur under the null hypothesis — that is, assuming there is no true effect of the bonus. This corresponds to option A: "Calculate the probability of a difference of 10." Typically, this is executed through a hypothesis test, such as a t-test, which calculates a p-value representing the likelihood of observing a difference as large or larger than the one observed, assuming the null hypothesis is true. This step directly tests the significance of the result in question.

Finally, to understand the robustness and reliability of this analysis, the experiment can be repeatedly performed or simulated many times, which aligns with option E: "Run the experiment many times." Although in practice, repeated actual experiments may not always be feasible, this step is analogous to conducting a simulation or permutation test to confirm the stability of the statistical inference.

In summary, the correct order of steps to determine if the observed difference is statistically significant is as follows:

1. C: Randomly separate the employees’ individual results into two groups.

2. D: Calculate the mean of each group.

3. B: Calculate the difference of the means.

4. A: Calculate the probability of a difference of 10.

5. E: Run the experiment many times.

This sequence ensures a methodical approach, starting from data organization, moving through descriptive statistics, to inferential probability calculations, and finally, validation through repeated testing or simulations. Following these steps adheres to standard statistical practices for hypothesis testing in experimental research.

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