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# Inference

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One factor in low productivity is the amount of time wasted by workers. Wasted time includes time spent cleaning up mistakes, waiting for more material and equipment, and performing any other activity not related to production. In a project designed to examine the problem, an operations management consultant took a survey of 200 workers in companies that were classified as successful (on the basis of their annual profits) and 200 workers from unsuccessful companies. The amount of time (in hours) wasted during a standard work week was recorded for each worker. These data are stored in column 1(successful companies) and column 2 (unsuccessful companies) file productivity

a. Do these data provide enough evidence at the 1% significance level to infer that the amount of time wasted in unsuccessful firms exceeds that of successful ones?
b. Estimate with 95% confidence how much more time is wasted in unsuccessful firms than in successful ones.

##### Solution Summary

One factor in low productivity is the amount of time wasted by workers. Wasted time includes time spent cleaning up mistakes, waiting for more material and equipment, and performing any other activity not related to production. In a project designed to examine the problem, an operations management consultant took a survey of 200 workers in companies that were classified as successful (on the basis of their annual profits) and 200 workers from unsuccessful companies. The amount of time (in hours) wasted during a standard work week was recorded for each worker. These data are stored in column 1(successful companies) and column 2 (unsuccessful companies) file productivity

a. Do these data provide enough evidence at the 1% significance level to infer that the amount of time wasted in unsuccessful firms exceeds that of successful ones?
b. Estimate with 95% confidence how much more time is wasted in unsuccessful firms than in successful ones.

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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