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 № Condition free/or 0.5\$ m43 A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results. ..a. Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? b. Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the .05 significance level. c. Develop the regression equation for effective heating based on wattage. d. Which heater looks like the “best buy” based on the size of theresidual? buy m44 A consumer organization wants to know whether there is a difference in the price of a particular toy at three different types of stores. The price of the toy was checked in a sample of five discount stores, five variety stores, and five department stores. The results are shown below. Use the .05 significancelevel. buy m45 A consumer watchdog organization is concerned about credit card debt. A survey of 10 young adults with credit card debt of more than \$2,000 showed they paid an average of just over \$100 per month against their balances. Listed below are the amounts each young adult paid last month. .. a. Compute the sample variance. b. Determine the sample standarddeviation. buy m46 A dog trainer is exploring the relationship between the size of the dog (weight in pounds) and its daily food consumption (measured in standard cups). Below is the result of a sample of 18 observations. .. a. Compute the correlation coefficient. Is it reasonable to conclude that the correlation in the population is greater than zero? Use the .05 significance level. b. Develop the regression equation for cups based on the dog’s weight. How much does each additional cup change the estimated weight of the dog? c. Is one of the dogs a big undereater orovereater? m47 A federal study reported that 7.5% of the U.S. workforce has a drug problem. A drug enforcement official for the state of Indiana wished to investigate this statement. In her sample of 20 employed workers: a. How many would you expect to have a drug problem? What is the standard deviation? b. What is the likelihood that none of the workers sampled has a drug problem? c. What is the likelihood at least one has a drug problem? m48 A film alliance used a random sample of 50 U.S. citizens to estimate that the typical American spent 78 hours watching videos and DVDs last year. The standard deviation of this sample was 9 hours. a. Develop a 95% confidence interval for the population mean number of hours spent watching videos and DVDs last year. b. How large a sample should be used to be 90% confident the sample mean is within 1.0 hour of the population mean? m49 A firm will promote two employees out of a group of six men and three women. a. List all possible outcomes. b. What probability concept would be used to assign probabilities to the outcomes? m50 A goal of financial literacy for children is to learn how to manage money wisely. One question is: How much money do children have to manage? A recent study by Schnur Educational Research Associates randomly sampled 15 children between 8 and 10 years old and 18 children between 11 and 14 years old and recorded their monthly allowance. Is it reasonable to conclude that the mean allowance received by children between 11 and 14 years is more than the allowance received by children between 8 and 10 years? Use the .01 significance level. What is thep-value? buy m51 A group of department store buyers viewed a new line of dresses and gave their opinions of them. The results were:  Because the largest number (47) indicated the new line is outstanding, the head designer thinks that this is a mandate to go into mass production of the dresses. The head sweeper (who somehow became involved in this) believes that there is not a clear mandate and claims that the opinions are evenly distributed among the six categories. He further states that the slight differences among the various counts are probably due to chance. Test the null hypothesis that there is no significant difference among the opinions of the buyers. Test at the .01 level of risk. Follow a formal approach; that is, state the null hypothesis, the alternate hypothesis, and soon. m52 A highway employee performed a regression analysis of the relationship between the number of construction work-zone fatalities and the number of unemployed people in a state. The regression equation is Fatalities 5 12.7 1 0.000114 (Unemp). Some additional output is:  a. How many states were in the sample? b. Determine the standard error of estimate. c. Determine the coefficient of determination. d. Determine the correlation coefficient. e. At the .05 significance level, does the evidence suggest there is a positive association between fatalities and the numberunemployed? buy m53 A large company is organized into three functional areas: manufacturing, marketing, and research and development. The employees claim that the company pays women less than men for similar jobs. The company randomly selected four males and four females in each area and recorded their weekly salaries in dollars.  a. Draw the interaction graph. Based on your observations, is there an interaction effect? Based on the graph, describe the interaction effect of gender and area on salary. b. Compute an ANOVA with statistical software, and use the 0.05 level to test for gender, area, and interaction effects on salary. Report the statistical results. c. Compare the male and female mean sales for each area using statistical techniques. What do you recommend to thedistributor? buy m54 (a) Let A C Rn be an open set such that boundary A is an (n - 1) -dimensional manifold. Show that N = AU boundary A is an -dimensional manifold with boundary. (It is well to bear in mind the following example: if A = {x ЄRn}: |x| < 1 or 1 < |x| < 2}, then N = AU boundary A is a manifold with boundary, but ∂ N ≠ boundary A. (b) Prove a similar assertion for an open subset of an n-dimensional manifold. buy m55 A machine is set to produce tennis balls so the mean bounce is 36 inches when the ball is dropped from a platform of a certain height. The production supervisor suspects that the mean bounce has changed and is less than 36 inches. As an experiment, a sample of 12 balls was dropped from the platform and the mean height of the bounce was 35.5 inches, with a standard deviation of 0.9 inch. At the .05 significance level, can the supervisor conclude that the mean bounce height is less than 36 inches? (a) The null and the alternate hypotheses, (b) The decision rule, and (c) The decision regarding the null hypothesis, (d) Then interpret the result. buy m56 A manufacturer of window frames knows from long experience that 5% of the production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 20 window frames: a. None will need adjustment? b. At least one will need adjustment? c. More than two will need adjustment? buy m57 A multiple regression equation yields the following partial results.  a. What is the total sample size? b. How many independent variables are being considered? c. Compute the coefficient of determination. d. Compute the standard error of estimate. e. Test the hypothesis that none of the regression coefficients is equal to zero. Let α =.05. buy m58 A national grocer’s magazine reports the typical shopper spends 8 minutes in line waiting to check out. A sample of 24 shoppers at the local Farmer Jack’s showed a mean of 7.5 minutes with a standard deviation of 3.2 minutes. Is the waiting time at the local Farmer Jack’s less than that reported in the national magazine? Use the .05 significance level. buy m59 A National Park Service survey of visitors to the Rocky Mountain region revealed that 50% visit Yellowstone Park, 40% visit the Tetons, and 35% visit both. a. What is the probability a vacationer will visit at least one of these attractions? b. What is the probability .35 called? c. Are the events mutually exclusive? Explain. buy m60 A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were:  At the .02 level of significance, can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Determine thep-value. buy m61 A new assembly-line procedure to increase production has been suggested by Mr. Mump. To test whether the new procedure is superior to the old procedure, a random sample of 15 assembly-line workers was selected. The number of units produced in an hour under the old procedure was determined, then the new Mump procedure was introduced. After an appropriate break-in period, their production was measured again. The results were:  At the .05 significance level, can we conclude the production is greater using the Mump method? a. State the null and alternate hypotheses. b. State the decision rule. c. Arrive at a decision regarding the nullhypothesis. buy m62 A new industrial oven has just been installed at Piatt Bakery. To develop experience regarding the oven temperature, an inspector reads the temperature at four different places inside the oven each half hour starting at 8:00 a.m. The last reading was at 10:30 a.m., for a total of six samples. The first reading, taken at 8:00 a.m., was 340 degrees Fahrenheit. (Only the last two digits are given in the following table to make the computations easier.)  .:. a. On the basis of this initial experience, determine the control limits for the mean temperature. Determine the grand mean. Plot the experience on a chart. b. Interpret the chart. Does there seem to be a time when the temperature is out of control? buy

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