1. Fasten-it-All produces wood and metal screws. The screws must be manufactured to within certain tolerances or they are considered defective. A machine that produces more than 1.1% defective screws must be shut down. To test Machine 1, a QC inspector randomly samples 1000 screws. The QC inspector’s random sample of 1000 screws contains 7 defects.

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CHAPTER 2 EXERCISES
1. Fasten-it-All produces wood and metal screws. The screws must be
manufactured to within certain tolerances or they are considered defective. A
machine that produces more than 1.1% defective screws must be shut down. To test
Machine 1, a QC inspector randomly samples 1000 screws. The QC inspector’s
random sample of 1000 screws contains 7 defects.
a. Based on this sample, compute by hand (using the normal approximation to the
binomial) and interpret a 95% confidence interval for Machine 1’s defect rate. Confirm
your result with Minitab.
b. Based on the 95% confidence interval computed in a, what recommendation
would you make regarding whether Machine 1 should be shut down?
c. Suppose the QC inspector had, instead, taken a sample of 3000 screws and
found 21 to be defective. Based on this sample, compute by hand (using the normal
approximation to the binomial) and interpret a 95% confidence interval for Machine
1’s defect rate? Confirm your result with Minitab.
d. Based on the 95% confidence interval computed in c, what recommendation
would you make regarding whether Machine 1 should be shut down?
e. Using Minitab, compute with the Exact method, the 95% confidence intervals for
parts a and c. How do they compare with your 95% CI’s using the normal
approximation? Why should the Exact method be used whenever possible?
2. We are farming Japanese koi fish, an ornamental type of carp used to decorate
ponds and water displays. An interested buyer will buy our farm at a great price for

2. us if he is 95% confident that our breeding methods produce at least 50% Kohaku koi,
a particularly coveted type of the fish. That determination will be based on a lower
bound computed with the Exact Method. The buyer’s people randomly sample 55 koi
fish from our pond and obtain 35 Kohaku. Will we have a sale?
3. To gauge immediate interest in a possible re-match, 500 pay-per-view buyers of
the recent Mayweather-Pacquiao fight were asked right after the fight if they would be
likely to buy pay-per-view for a re-match. The results are recorded in raw form in the
dataset: ReMatch (0 indicates “No.” 1 indicates “Yes.”) Use Minitab to compute a
95% confidence interval for the proportion of pay-per-view customers who will buy a
re-match. Interpret this confidence interval.
4. A candidate for a US Representative seat from Indiana hires a polling firm to
gauge her percentage of support among voters in her district. a. If a​ 95%
confidence interval with a margin of error of no more than 0.04 is desired, give a close
estimate of the minimum sample size necessary to achieve the desired margin of
error.
b. If a ​95% confidence interval with a margin of error of no more than 0.02 is
desired, give a close estimate of the minimum sample size necessary to achieve the
desired margin of error.
Test and CI for One Proportion
Sample X N Sample p ___% Lower Bound
1 34 50 0.680000 0.555377
Test and CI for One Proportion
Sample X N Sample p ___% Lower Bound

3. 1 34 50 0.680000 0.581029
5. We are operating a highly profitable catfish farm. To assess the proportion of
our fish that are over 9.5 lbs., we randomly sample 50 and get 34 heavier than 9.5 lbs.
Above, we have used the Exact method to compute both the 90% and 95% Lower
Bounds.
a. Which of the above is the 90% Lower Bound?
b. Give a correct interpretation of the 90% Lower Bound.
c. Based on this sample, use the normal approximation to the binomial to compute a
90% confidence interval for the proportion of our catfish that weigh more than 9.5 lbs.
d. Give a correct interpretation of this interval.