1. A sample of 15 manufacturers of electronics components reported an average of $20.3 million in backlogged orders, with a standard deviation of $6.45 million. Assume that backlog is approximately normally distributed. Generate a 95% confidence interval(or interval estimate) on mean backlog for the entire electronics component manufacturing industry, consisting of 2,550 companies.
2. A computer manufacturer is considering the use of a new process for assembling wiring harnesses. It tested 160 of these harnesses assembled by the new process, and found 4 defects. It would like to offer a warranty that its process will yield a very high reliability. Conduct ahypothesis testat the 5% significance level that the manufacturer is achieving at least 98 percent reliability. What do you conclude? Is this a viable claim?
3. A manufacturing company fabricates tight-tolerance, 0.5500-inch-diameter rocker arms for one of its products. Samples of 50 rocker arms are taken each day to be certain the machine is still functioning properly. Today's sample yielded a mean diameter of 0.5535 inches with a standard deviation of 0.03 inches. Perform ahypothesis test at the 10% significance level that the machine remains in tolerance, and has not begun making defective rocker arms that are either too large or too small in diameter. Provide both Critical Value and p-value solutions. Should the manufacturer stop the machine and repair it, or continue?
4. In the problem above, what sample size will the manufacturing company need to ensure it achieves its targets for Type 1 error of 1% against the mean value of 0.5500, and for a Type 2 error of 5% against an alternative mean value of 0.5520 inches? Is n=50 sufficient?
5. If 50 manufacturers are drawn from the 2,550 companies in the industry, and 15 of them are qualified ISO 9001 manufacturers, form an interval estimate with 90 percent confidence on thepercent of manufacturers who are ISO 9001 qualified.
6. We want to estimate the skid distance of a Firestone radial tire of known tread design. Suppose we have computed the population mean and variance to be 50 feet and 25 feet-squared. (a) Compute the minimum sample size required for a 95 percent-confidencemargin of error of two inches on the mean skid distance.
(b) If we test 50 tires and find the sample mean is 52.3 feet, form an interval estimate for the population mean.
7. A polling company wants to be very careful in its upcoming opinion survey on an upcoming tax proposition. To ensure precision, it is willing to sample as many respondents as is necessary. In a small pilot survey of 100 residents, it found that only 17 of themsaid they intended to vote“yes”on the proposition. How large does the sample size need to be in the full survey to achieve 2 percent margin of error with 99 percent confidence?
8. The following data represent crop yields in bushels per acre versus quantity of fertilizer applied in pounds per acre:
Fertilizer applied Yield
(a) Graph the scatter diagram. Is a linear regression model appropriate? (5)
(b) Compute the regression coefficients “b0” and “b1”, state the regression equation, and graph the regression line on the scatter diagram. (10)
(c) If 475 pounds per acre were applied, what would you predict the yield in bushels per acre to be? (5)
(d) Compute the coefficient of determination and correlation coefficient of the regression. What does it tell you about the accuracy of your answer in part (b)? (5)