A automobile manufacturing company is conducting research in an attempt to predict the model of mobile design consumers will desire in the year 2025. Is this applied or basic research?
Mr. B, a well-known rancher and not so well-known part-time cattle rustler, has 20 head of cattle ready for market. Sixteen of these are his own and consequently bear his own brand. The other four bear foreign brands. Mr. B knows that the brand inspector at the market place checks the brand of 20 percent of the cattle in any shipment. He has two trucks, one of which will haul all 20 cattle at once and the other will haul ten at a time. Mr. B feels that he has four different strategies to follow in his attempt to market the cattle without getting caught. The first is to sell all twenty head at once, the others are to sell ten head on two different occasions, putting all four stolen cattle in one set of ten or three head in one shipment and one in the other, or two head in each of the shipments of ten. Which strategy will minimize Mr. B’s probability of getting caught, and what is his prob. Of getting caught under each category?
A friend asks you for a loan of $1,000 and offers to pay you back at the rate of $90 per month for 12 months. a. Using an annual interest rate of 10%, find the net present value(to you) of loaning your friend the money. Repeat using an interest rate of 20%. b. Find an interest rate that gives a net present value of 0.
Robin Briggs does not have access to the same investments as union . In fact, the best available alternative is to invest in a security earning 10% over next 7 years. Using this interest rate, what is Brigg’s net present value of the offer made by the union? Should Briggs accept the offer?
Wearing a Uniform to Work: The website fox6now.com held an online poll in June 2015 asking “What do you think about the concept of having an everyday uniform for work, like Steve Jobs did?”
- Explain how sample bias is likely to be present in this study.
- What part of the question might bring in wording bias? How do you expect that part to bias the results?
There are other out-of-control rules that are sometimes used with x¯ charts. One is “15 points in a row within the 1σ level.” That is, 15 consecutive points fall between μ−σ/n and μ+σ/n. This signal suggests either that the value of σ used for the chart is too large or that careless measurement is producing results that are suspiciously close to the target. Find the probability that the next 15 points will give this signal when the process remains in control with the given μ and σ
Previously, control of the process was based on categorizing the thickness of each film inspected as satisfactory or not. Steady improvement in process quality has occurred, so that just 15 of the last 5000 films inspected were unsatisfactory.
(a) What type of control chart would be used in this setting, and what would be the control limits for a sample of 100 films?
(b) The chart in part (a) is of little practical value at current quality levels. Explain why.
The specifications call for film thickness 830 ± 25 mm × 10−4.
(a) What is the estimate σ^ of the process standard deviation based on the sample standard deviations (after removing Samples 1 and 10)? Estimate the capability ratio Cp and comment on what it says about this process.
(b) Because the process mean can easily be adjusted, Cp is more informative than Cpk. Explain why this is true.
(c) The estimate of Cp from part (a) is probably too optimistic as a description of the film produced. Explain why
Interviews with the operators reveal that in Samples 1 and 10 mistakes in operating the interferometer resulted in one high-outlier thickness reading that was clearly incorrect. Recalculate x¯ and s after removing Samples 1 and 10. Recalculate UCL for the s chart and add the new UCL to your s chart from the previous exercise. Control for the remaining samples is excellent. Now find the appropriate center line and control limits for an x¯ chart, make the x¯ chart, and comment on control.
At the present time, about 5 out of every 1000 lots of material arriving at a plant site from outside vendors are rejected because they do not meet specifications. The plant receives about 350 lots per week. As part of an effort to reduce errors in the system of placing and filling orders, you will monitor the proportion of rejected lots each week. What type of control chart will you use? What are the initial center line and control limits?
Wearing a Uniform to Work: The website fox6now.com held an online poll in June 2015 asking “What do you think about the concept of having an everyday uniform for work, like Steve Jobs did?”
- Explain how sample bias is likely to be present in this study.
- What part of the question might bring in wording bias? How do you expect that part to bias the results?
There are other out-of-control rules that are sometimes used with x¯ charts. One is “15 points in a row within the 1σ level.” That is, 15 consecutive points fall between μ−σ/n and μ+σ/n. This signal suggests either that the value of σ used for the chart is too large or that careless measurement is producing results that are suspiciously close to the target. Find the probability that the next 15 points will give this signal when the process remains in control with the given μ and σ
Previously, control of the process was based on categorizing the thickness of each film inspected as satisfactory or not. Steady improvement in process quality has occurred, so that just 15 of the last 5000 films inspected were unsatisfactory.
(a) What type of control chart would be used in this setting, and what would be the control limits for a sample of 100 films?
(b) The chart in part (a) is of little practical value at current quality levels. Explain why.
The specifications call for film thickness 830 ± 25 mm × 10−4.
(a) What is the estimate σ^ of the process standard deviation based on the sample standard deviations (after removing Samples 1 and 10)? Estimate the capability ratio Cp and comment on what it says about this process.
(b) Because the process mean can easily be adjusted, Cp is more informative than Cpk. Explain why this is true.
(c) The estimate of Cp from part (a) is probably too optimistic as a description of the film produced. Explain why
Interviews with the operators reveal that in Samples 1 and 10 mistakes in operating the interferometer resulted in one high-outlier thickness reading that was clearly incorrect. Recalculate x¯ and s after removing Samples 1 and 10. Recalculate UCL for the s chart and add the new UCL to your s chart from the previous exercise. Control for the remaining samples is excellent. Now find the appropriate center line and control limits for an x¯ chart, make the x¯ chart, and comment on control.
At the present time, about 5 out of every 1000 lots of material arriving at a plant site from outside vendors are rejected because they do not meet specifications. The plant receives about 350 lots per week. As part of an effort to reduce errors in the system of placing and filling orders, you will monitor the proportion of rejected lots each week. What type of control chart will you use? What are the initial center line and control limits?
What type of control chart or charts would you use as part of efforts to assess quality? Explain your choices.
(a) Time to get security clearance
(b) Percent of job offers accepted
(c) Thickness of steel washers
(d) Number of dropped calls per day
A manager who knows no statistics asks you, “What does it mean to say that a process is in control? Is being in control a guarantee that the quality of the product is good?” Answer these questions in plain language that the manager can understand.
Refer to the previous exercise. The time it takes from deciding to order a sandwich to receiving the sandwich will vary. List several common causes of variation in this time. Then list several special causes that might result in unusual variation
Previous exercise
Consider the process of calling in a sandwich order for delivery to your apartment. Make a flowchart of this process, making sure to include steps that involve Yes/No decisions
Refer to the previous two exercises. Here is another way to communicate the result: teen gamers are 65% more likely to play on consoles than adult gamers.
(a) Explain how the 65% is computed.
(b) Use the bootstrap to give a 95% confidence interval for this estimate.
(c) Based on this exercise and the previous two, which of the three ways is most effective for communicating the results? Give reasons for your answer
Previous two exercise
Refer to the previous exercise. In many settings, researchers prefer to communicate the comparison of two proportions with a ratio. For gamers who play on consoles, they would report that teens are 1.65 (89/54) times more likely to play on consoles. Use the bootstrap to give a 95% confidence interval for this ratio.
Previous exercise
A Pew survey compared adult and teen gamers on where they played games. For the adults, 54% of 1063 survey participants played on game consoles such as Xbox, PlayStation, and Wii. For teens, 89% of 1064 survey participants played on game consoles. Use the bootstrap to find a 95% confidence interval for the difference between the teen proportion who play on consoles and the adult proportion.