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About 102926 results. 1294 free access solutions
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| m724 | Patient response to a generic drug to control pain is scored on a 5-point scale, where a 5 indicates complete relief. Historically the distribution of scores is
1 2 3 4 5
0.05 0.1 0.2 0.25 0.4
Two patients, assumed to be independent, are each scored.
(a) What is the probability mass function of the total score?
(b) What is the probability mass function of the average score? |
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| m725 | Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 20 stations last Tuesday, the correlation was .78. At the .01 significance level, is the correlation in the population greater than zero? |
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| m726 | Pierre’s Restaurant announced that on Thursday night the menu would consist of unusual gourmet items, such as squid, rabbit, snails from Scotland, and dandelion greens. As part of a larger survey, a sample of 81 regular customers was asked whether they preferred the regular menu or the gourmet menu. Forty-three preferred the gourmet menu. At the .02 level, can we conclude the customers preferred the gourmet menu? |
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| m727 | Pittsburgh Paints wishes to test an additive formulated to increase the life of paints used in the hot and arid conditions of the Southwest. The top half of a piece of wood was painted using the regular paint. The bottom half was painted with the paint including the additive. The same procedure was followed for a total of 10 pieces. Then each piece was subjected to brilliant light. The data, the number of hours each piece lasted before it faded beyond a certain point, follow:
Using the .05 significance level, determine whether the additive is effective in prolonging the life of the paint.
(a) The null and the alternate hypotheses,
(b) The decision rule, and
(c) The decision regarding the null hypothesis,
(d) Then interpret theresult. |
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| m728 | Place these variables in the following classification tables. For each table, summarize your observations and evaluate if the results are generally true. For example, salary is reported as a continuous quantitative variable. It is also a continuous ratio-scaled variable.
a. Salary
b. Gender
c. Sales volume of MP3 players
d. Soft drink preference
e. Temperature
f. SAT scores
g. Student rank in class |
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| m729 | Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 12 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. An inspector chooses 3 parts from among the 12 at random. Two cavities are affected by a temperature malfunction that results in parts that do not conform to specifications.
(a) What is the probability that the inspector finds exactly one nonconforming part?
(b) What is the probability that the inspector finds at least one nonconforming part? |
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| m730 | Plywood Inc. reported these returns on stockholder equity for the past 5 years: 4.3, 4.9, 7.2, 6.7, and 11.6. Consider these as population values.
a. Compute the range, the arithmetic mean, the variance, and the standard deviation.
b. Compare the return on stockholder equity for Plywood Inc. with that for Dennis Indus-tries cited in Exercise 44. |
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| m731 | PNC Bank Inc., which has its headquarters in Pittsburgh, reported $17,446 (million) in commercial loans in 1995, $19,989 in 1997, $21,468 in 1999, $21,685 in 2000, $15,922 in 2002, $18,375 in 2004, $54,818 in 2009, and $83,040 in 2012. Using 1995 as the base, develop a simple index of commercial loans for the years 2002, 2004, 2009, and 2012. |
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| m732 | Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 35.0 hours and a standard deviation of 5.5 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 25 batteries.
a. What can you say about the shape of the distribution of the sample mean?
b. What is the standard error of the distribution of the sample mean?
c. What proportion of the samples will have a mean useful life of more than 36 hours?
d. What proportion of the sample will have a mean useful life greater than 34.5 hours?
e. What proportion of the sample will have a mean useful life between 34.5 and 36.0 hours? |
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| m733 | Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 cards, and 20 are selected without replacement for functional testing.
(a) If 20 cards are defective, what is the probability that at least 1 defective card is in the sample?
(b) If 5 cards are defective, what is the probability that at least 1 defective card appears in the sample? |
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| m734 | Proactine, a new medicine for acne, is claimed by the manufacturer to be 80% effective. It is applied to the affected area of a sample of 15 people. What is the probability that:
a. All 15 will show significant improvement?
b. Fewer than 9 of 15 will show significant improvement?
c. 12 or more people will show significant improvement? |
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| m736 | Professor Bert Forman believes the students who complete his examinations in the shortest time receive the highest grades and those who take the longest to complete them receive the lowest grades. To verify his suspicion, he assigns a rank to the order of finish and then grades the examinations. The results are shown below:
Convert the test scores to a rank and find the coefficient of rank correlation between the order of completion and the rank of the test score. At the .05 significance level, can Professor Forman conclude there is a positive association between the order of finish and the testscores? |
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| m737 | Prove that a k-dimensional (vector) subspace of Rn is a k-dimensional manifold. |
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| m738 | Prove that if f: Rn -> Rm is differentiable at a € Rn, then it is continuous at a. |
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| m739 | Prove a partial converse to Theorem 5-1: If MCRn is a k-dimensional manifold and xЄM, then there is an open set A C Rn containing and a differentiable function g: A ->Rn-k such that A∩M = g-1 (0) and g1 (y) has rank n – k when g(y) = 0. |
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| m740 | Prove that R = [a1, b1] x..x [an, bn] is not of content if ai < bi for i =1. n. |
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| m741 | A quality characteristic of interest for a coffee-bag-filling process is the weight of the coffee in the individual bags. If the bags are under filled, two problems arise. First, customers may not be able to brew the coffee to be as strong as they wish. Second, the company may be in violation of the truth-in-labeling laws. In this example, the label weight on the package indicates that, on average, there are 5.45 grams of coffee in a bag. If the average amount of coffee in a bag exceeds the label weight, the company is giving away product. Getting an exact amount of coffee in a bag is problematic because of variation in the temperature and humidity inside the factory, differences in the density of the coffee, and the extremely fast filling operation of the machine (approximately 170 bags a minute). The following table provides the weight in grams of a sample of 50 bags produced in one hour by a single machine:
a. Compute the arithmetic mean and median.
b. Compute the first quartile and third quartile.
c. Compute the range, interquartile range, variance, standard deviation, and coefficient of variation.
d. Interpret the measures of central tendency within the context of this problem. Why should the company producing the coffee bags be concerned about the central tendency?
e. Interpret the measures of variation within the context of this problem. Why should the company producing the coffee bags be concerned about variation? |
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| m742 | Quick-print firms in a large downtown business area spend most of their advertising dollars on displays on bus benches. A research project involves predicting monthly sales based on the annual amount spent on placing ads on bus benches. A sample of quick-print firms revealed these advertising expenses and sales:
a. Draw a scatter diagram.
b. Determine the correlation coefficient.
c. What is the coefficient of determination?
d. Compute the regression equation.
e. Estimate the monthly sales of a quick-print firm that spends $4,500 on bus bench advertisements.
f. Summarize yourfindings. |
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| m743 | Random samples of five were selected from each of three populations. The sum of squares total was 100. The sum of squares due to the treatments was 40.
a. Set up the null hypothesis and the alternate hypothesis.
b. What is the decision rule? Use the .05 significance level.
c. Complete the ANOVA table, what is the value of F?
d. What is your decision regarding the null hypothesis? |
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| m744 | Ray Anderson, owner of Anderson Ski Lodge in upstate New York, is interested in forecasting the number of visitors for the upcoming year. The following data are available, by quarter, from the first quarter of 2007 to the fourth quarter of 2013. Develop a seasonal index for each quarter. How many visitors would you expect for each quarter of 2014, if Ray projects that there will be a 10% increase from the total number of visitors in 2013? Determine the trend equation, project the number of visitors for 2014, and seasonally adjust the forecast. Which forecast would youchoose? |
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