T7 SOLUTIONS_Combined_1_2018.pdf

C what if the assumption of a normal distribution was

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(c) What if the assumption of a normal distribution was incorrect? What will happen to your answers for Parts (a) and (b)? Which, if either, of your answers above would be changed by this information, and why? If the assumption that the distribution of the content of the soft drink bottles follows a normal distribution is incorrect, it would change the answers to part (a) and (b). We would not be able to calculate the answer to (a) without the assumption of a normal distribution as it is essential for standardising this part. For part (b), the central limit theorem cannot be invoked as the sample size of 6 is not sufficiently large. In this case, we cannot assume that the distribution of distribution is approximately normal.
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ETF1100 Business Statistics SOLUTIONS Tutorial 7 4 Confidence Interval Estimation USE TABLES FOR ALL OF THE FOLLOWING QUESTIONS Q7.3 The ‘Steel Housings’ Problem: The following question (both parts (a) and (b) have already been answered for you so that you can answer the very important question in part (c) . Please read through these answers thoroughly and then answer Q7.3 (c) very carefully. (a) A manufacturing company produces steel housings for electrical equipment. The main component of the housing is a steel trough made out of a 2mm steel coil. The width of the troughs is critical because of weatherproofing in outdoor situations. A sample of 49 troughs was found to have a mean of 204.209 mm. Assuming that the population standard deviation is 0.46mm, calculate a 95% confidence interval for the mean width of the troughs. Show your answers to two decimal places . Show ALL your working and remember to always interpret your interval in the context of this question. Solution: Let X=width of trough (mm) Assume n = 49, 1- α =0.95, so α =0.05, The 95% confidence interval for : Z: -1.96 1.96 95% .46 0 , ~ N X 209 . 204 X 46 . 0 96 . 1 Z Z Z 025 . 0 2 05 . 0 2 0.46 0.46 204.209 1.96X 204.209 1.96X 49 49 204.209 1.96X0.0657 204.209 1.96X0.0657 204.209 0.1288 204.209 0.1288          n Z X n Z X 2 2
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ETF1100 Business Statistics SOLUTIONS Tutorial 7 5 Interpretation: We are 95% confident that the true mean width of the steel troughs lies between 204.08mm and 204.34mm. (b) Repeat Q7.3(a) , but this time, assume that the population standard deviation is UNKNOWN . The standard deviation of the sample of 49 was found to be 0.461146mm. Also this time, use Excel to find the appropriate critical values .
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