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free/or 0.5$ |
| m825 | Research by the First Bank of Illinois revealed that 8% of its customers wait more than 5 minutes for a teller in a bank lobby. Management considers this reasonable and will not add more tellers unless the proportion waiting longer than 5 minutes becomes larger than 8%. The branch manager at the Litchfield Branch believes that the wait is longer than the standard at her branch and requested additional part-time tellers. To support her request, she found that, in a sample of 100 customers, 10 waited more than 5 minutes. At the .01 significance level, is it reasonable to conclude that more than 8% of the customers wait more than 5 minutes? |
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| m826 | Research in the gaming industry showed that 10% of all slot machines in the United States stop working each year. Short’s Game Arcade has 60 slot machines and only 3 failed last year. At the .05 significance level, test whether these data contradict the research report.
a. Why can you employ z as the test statistic?
b. State the null and alternate hypotheses.
c. Evaluate the test statistic and make the decision.
d. What is the p-value and what does that imply? |
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| m827 | Residents of the state of South Carolina earned a total of $69.5 billion in adjusted gross income. Seventy-three percent of the total was in wages and salaries; 11% in dividends, interest, and capital gains; 8% in IRAs and taxable pensions; 3% in business income pensions; 2% in Social Security; and the remaining 3% from other sources. Develop a pie chart depicting the breakdown of adjusted gross income. Write a paragraph summarizing the information. |
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| m828 | Robert Altoff is vice president for engineering for a manufacturer of household washing machines. As part of new product development, he wishes to determine the optimal length of time for the washing cycle. A part of the development is to study the relationship between the detergent used (four brands) and the length of the washing cycle (18, 20, 22, or 24 minutes). In order to run the experiment, 32 standard household laundry loads (having equal amounts of dirt and the same total weights) are randomly assigned to the 16 detergent–washing cycle combinations. The results (in pounds of dirt removed) are shown below.
a. Draw an interaction plot of the detergent means by cycle time.
b. Compute the ANOVA with statistical software and, using the .05 significance level, test the interaction effect of brand and cycle time on “dirt removed.”
c. Based on your results in part (b), conduct the appropriate tests of hypotheses for differences in factor means.
d. Interpret the results in a briefreport. |
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| m829 | A robotic insertion tool contains 10 primary components. The probability that any component fails during the warranty period is 0.01. Assume that the components fail independently and that the tool fails if any component fails. What is the probability that the tool fails during the warranty period? |
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| m830 | Rutter Nursery Company packages its pine bark mulch in 50-pound bags. From a long history, the production department reports that the distribution of the bag weights follows the normal distribution and the standard deviation of this process is 3 pounds per bag. At the end of each day, Jeff Rutter, the production manager, weighs 10 bags and computes the mean weight of the sample. Below are the weights of 10 bags from today’s production.
a. Can Mr. Rutter conclude that the mean weight of the bags is less than 50 pounds? Use the .01 significance level.
b. In a brief report, tell why Mr. Rutter can use the z distribution as the test statistic.
c. Compute thep-value. |
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| m831 | Sales of roof material, by quarter, for 2007 through 2013, by Carolina Home Construction Inc. are shown below (in $000).
a. Determine the typical seasonal patterns for sales using the ratio-to-moving-average method.
b. Deseasonalize the data and determine the trend equation.
c. Project sales for 2014 using the trend equation and seasonally adjust these values to find the predicted sales for each quarter. |
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| m832 | Sally’s Software Inc. is a rapidly growing supplier of computer software to the Sarasota area. Sales for the last 5 years, 2009 to 2013, are given below.
Sales
Year ($ millions)
2009 ......... 1.1
2010 ......... 1.5
2011 ......... 2.0
2012 ......... 2.4
2013 ......... 3.1
a. Determine the logarithmic trend equation.
b. By what percent did sales increase, on the average, during the period?
c. Estimate sales for the year 2016. |
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| m833 | Sam Steward is a freelance Web page designer. Listed below are his yearly wages for several years between 2007 and 2013. Also included is an industry index for Web page designers that reports the rate of wage inflation in the industry. This index has a base period of 1995.
Compute Sam’s real income for the selected years during the six-year period. Did his wages keep up with inflation, or did he loseground? |
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| m834 | A sample of three calculators is selected from a manufacturing line, and each calculator is classified as either defective or acceptable. Let A, B, and C denote the events that the first, second, and third calculators respectively, are defective.
(a) Describe the sample space for this experiment with a tree diagram. Use the tree diagram to describe each of the following events:
(b) A
(c) B
(d) A ∩ B
(e) B U C |
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| m835 | A sample of two items is selected without replacement from a batch. Describe the (ordered) sample space for each of the following batches:
(a) The batch contains the items {a, b, c, d}.
(b) The batch contains the items {a, b, c, d, e, f, g}.
(c) The batch contains 4 defective items and 20 good items.
(d) The batch contains 1 defective item and 20 good items. |
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| m836 | A sample of two printed circuit boards is selected without replacement from a batch. Describe the (ordered) sample space for each of the following batches:
(a) The batch contains 90 boards that are not defective, 8 boards with minor defects, and 2 boards with major defects.
(b) The batch contains 90 boards that are not defective, 8 boards with minor defects, and 1 board with major defects. |
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| m837 | A sample preparation for a chemical measurement is completed correctly by 25% of the lab technicians, completed with a minor error by 70%, and completed with a major error by 5%.
(a) If a technician is selected randomly to complete the preparation, what is the probability it is completed without error?
(b) What is the probability that it is completed with either a minor or a major error |
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| m838 | A sample space contains 20 equally likely outcomes.
If the probability of event A is 0.3, how many outcomes are in event A? |
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| m839 | A sampled injection-molded part could have been produced in either one of two presses and in any one of the eight cavities in each press. |
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| m840 | Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X denote the number of parts in the sample of 20 that require rework. A process problem is suspected if X exceeds its mean by more than three standard deviations.
(a) If the percentage of parts that require rework remains at 1%, what is the probability that X exceeds its mean by more than three standard deviations?
(b) If the rework percentage increases to 4%, what is the probability that X exceeds 1?
(c) If the rework percentage increases to 4%, what is the probability that X exceeds 1 in at least one of the next five hours of samples? |
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| m841 | Samples of a cast aluminum part are classified on the basis of surface finish (in micro inches) and length measurements. The results of 100 parts are summarized as follows: |
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| m842 | Samples of a cast aluminum part are classified on the basis of surface finish (in micro inches) and length measurements. The results of 100 parts are summarized as follows:
Length
Excellent Good
Surface excellent 80 2
Finish good 10 8
Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excellent length. Are events A and B independent? |
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| m843 | Samples of a cast aluminum part are classified on the basis of surface finish (in micro inches) and edge finish. The results of 100 parts are summarized as follows:
Edge finish
Excellent good Surface Excellent 80 2
Finish Good 10 8
(a) Let A denote the event that sample has excellent surface finish, and let B denote the event that a sample excellent edge finish, Determine the number of samples in A’ ∩ B, B’, and A U B.
(b) Assume that each of two samples is to be classified on the basis of surface finish, either excellent or good |
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| m844 | Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 samples are summarized as follows:
Conforms
Yes no
1 22 8
Supplier 2 25 5
3 30 10
Let A denote the event that a sample is from supplier 1, and let B denote the event that a sample conforms to specifications.
(a) Are events A and B independent?
(b) Determine |
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