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Hypothesis Testing and Tests for Independence for a construction company

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A construction company wants to determine if the likelihood of having an injury is related to the type of worker. Over the past decade the company has had an average total workforce of 2560 workers. On average 601 of these were tradesmen, 381 were apprentices and the rest were labourers. During that decade there was a total of 424 workers injured, 102 of these were tradesmen, 46 of these were apprentices, and the rest were labourers.

1) Calculate the number from this data that can be used to test for independence.

2)what is the critical value at the 1% significance level if the null hypothesis is that whether someone has an accident is independent of the type of worker?

3)We should reject the null hypothesis and conclude that the type of worker and whether or not they had an accident are not independent if the value calculated in Question (1) is:
a) less than the value in Question (2).
b) greater than the value in Question (2).

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Solution Summary

This solution explains how to construct and evaluate hypothesis tests for a construction company considering the impacts of job roles on injuries. There is also a part explaining how to test for independence.

Solution provided by:
Changping Wang, MA
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!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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