MAST 20005 : Automotive Supplier Places – Several Electrical Wires – Statistics Assignment Help

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Assignment Task :

Instructions: Questions labelled with ‘(R)’ require use of R. Please provide appropriate R commands and their output, along with sufficient explanation and interpretation of the output to demonstrate your understanding. Such R output should be presented in an integrated form together with your explanations. All other questions should be completed without reference to any R commands or output, except for looking up quantiles of distributions where necessary. Make sure you give enough explanation so your tutor can follow your reasoning if you happen to make a mistake. Please also try to be as succinct as possible. Each assignment will include marks for good presentation. 

1. (R) An interior automotive supplier places several electrical wires in a harness. A pull test measures the force required to pull spliced wires apart. A customer requires that each wire that is spliced into the harness withstand a pull force of 20 pounds. Let X be a random variable representing the pull force required to pull a spliced wire apart. The following are 20 observations of X: 

28.8 24.4 30.1 25.6 26.4 23.9 22.1 22.5 27.6 28.1 

20.8 27.7 24.4 25.1 24.6 26.3 28.2 22.2 26.3 24.4 

(a) Give basic summary statistics for these data and produce a box plot. Briefly comment on center, spread and shape of the distribution. 

(b) Assuming a normal distribution (with unknown mean and variance), compute maximum likelihood estimates for the parameters. 

(c) Draw a density histogram and superimpose a pdf for a normal distribution using the estimated parameters. 

(d) Draw a QQ plot to compare the data against the fitted normal distribution. Include a reference line. Comment on the fit of the model to the data. 

(e) Assume a normal distribution (with unknown mean and variance) for X. Find a one-sided 95% confidence interval that is a lower bound for the mean of X, and answer the question that whether the supplier meets the customer’s requirement

 

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