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Chi-statistical Analysis Of Seedless Golden Raisins Packaging

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A machine used for packaging seedless golden raisins is set so that their standard deviation in the weight of raisins packaged per box is 0.25 ounce. The operations manager wishes to test the machine setting and selects a sample of 30 consecutive raisin packages filled during the production process. Their weights are as recorded on the worksheet.

Weight
15.2
15
14.3
15.3
15.2
14.4
15.1
15.4
15.5
15.7
15.6
15.4
15.3
15.7
15.2
15
15.4
15.5
15.1
15.3
15.6
14.3
14.9
15.1
14.6
14.8
15.3
14.5
14.6
15.1

a. At the 0.05 level of significance, is there evidence that the population standard deviation differs from 0.25 ounces?

b. What assumptions are made in order to perform this test?
c. What are the degrees of freedom?

d) What is the chi-statistic?

This problem is to be solved with Excel using PHStat.

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Solution Summary

This solution conducts a hypothesis test by providing a null and alternative hypothesis, calculating the chi-statistic and comparing it to the p-value, and finally making a decision to accept or reject the null hypothesis on the machine's production process.

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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