Question

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, 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

Answer 1

(a)

Descriptive Statistics: X

Variable Mean StDev Variance Minimum Q1 Median Q3 Maximum
X 25.475 2.494 6.218 20.800 24.025 25.350 27.675 30.100

N for
Variable IQR Mode Mode Skewness Kurtosis
X 3.650 24.4 3 -0.05 -0.66

Almost symmetric and platykurtic.

(b)

$\hat{\mu}_{MLE}=\bar{x}=sample~mean= 25.475\\ \hat{\sigma}^2_{MLE}=\frac{1}{n}\sum_{i=1}^n(x_i-\bar{x})^2=6.218\\$

(c)

(d)

From the above plot it is observed that the data come from normal distribution.