The dimensions of 3877 manufactured parts were examined and 445 were found to have a length outside a specified tolerance range.
(a) Conduct a hypothesis test to investigate whether there is sufficient evidence to conclude that the probability of a part having a length outside the tolerance range is larger than 10%.
(b) Construct a one-sided 99% confidence interval that provides a lower bound on the probability of a part having a length outside the tolerance range.
It was also found that out of the 445 parts that had a length outside the specified tolerance range, 25 also had a width outside a specified tolerance range. Furthermore, out of the 3432 parts that had a length inside the specified tolerance range, it was found that 161 had a width outside the specified tolerance range.
(c) Use the Pearson chi-square statistic to test whether the acceptability of the length and the acceptability of the width of the parts are related to each other, or whether these two factors can be considered to be independent of each other.