1.Fasten-it-All produces wood screws. The screws must be manufactured to within certain tolerances or they are considered defective.Using 95% confidence, a machine that may be producing more than 1.42% defective screws must be shut down and adjusted.To test Machine 1, a QC inspector randomly samples 1200 screws.The QC inspector's random sample of 1200 screws contains 11 defective screws.

a.Based on this sample, compute by handusing 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 it is decided that an 90% confidence interval (using the normal approximation) can be used. Use Minitab to compute the confidence interval? What recommendation would be made about the machine?

d.Suppose the QC inspector had taken a sample of 2400 screws and found 22 that were defective.Compute by handusing the normal approximation to the binomial and interpret a 95% confidence interval for Machine 1's defect rate?Confirm your result with Minitab.

e.Based on the 95% confidence interval computed in d, what recommendation would you make regarding whether Machine 1 should be shut down?Briefly explain,how a sample with the same point estimate produced different recommendations in parts b and d.

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 us if he is 90% confident that our breeding methods produce at least 75% Kohaku koi, a particularly coveted type of the fish.The buyer has decided to make that determination based on alower bound computed with the Exact Method.The buyer's people randomly sample 40 koi fish from our pond and obtain 34 Kohaku.Will we have a sale?(Hint:Use Minitab to compute a 90% confidence lower bound with the Exact Method and interpret.)

3.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 a95% confidence intervalwith a margin of error of no more than 0.06 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved.(Remember to round up any result, if necessary.)

b.If a95% confidence intervalwith a margin of error of no more than 0.03 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved.(Remember to round up any result, if necessary.)

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-Extra Credit (5 pts) -Empirical Lower Bounds:Suppose 75% of our koi fish are Kohaku.

a.Not knowing this, we sample 40 and, as in Question 2, 34 are Kohaku. Using this sample result as the success probability, use Minitab to simulate the sampling of 40 fish 100 times. Sort the results from lowest to highest. Copy and paste from the worksheet column you used for storing the sorted results your lowest 11 results.

b.The 11^thresult can be considered a 90% lower bound, found empirically. How does yours compare with the lower bound found in Question 2 by the exact method? Does this empirical lower bound give an accurate estimate of the true population percentage of 75%?

c.Repeat part a using 75% as the success probability. How did changing the success probability affect your 90% empirical lower bound?