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free/or 0.5$ |
| m6768 | A random sample is obtained from a population with variance σ2 = 625 and the sample mean is computed. Test the null hypothesis H0: μ = 100 versus the alternative hypothesis H1: μ > 100 with α = 0.05. Compute the critical value x-barc and state your decision rule for the following options.
a. Sample size n = 25
b. Sample size n = 16
c. Sample size n = 44
d. Sample size n = 32 |
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| m6769 | A random sample of 10 corporate analysts was asked to rate, on a scale from 1 (very poor) to 10 (very high), the prospects for their own corporations and for the economy at large in the current year. The results obtained are shown in the accompanying table. Using the Wilcoxon signed rank test, discuss the proposition that in the aggregate corporate analysts are more optimistic about the prospects for their own companies than for the economy at large. |
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| m6770 | A random sample of 10 economists produced the following forecasts for percentage growth in real gross domestic product in the next year:
2.2 2.8 3.0 2.5 2.4 2.6 2.5 2.4 2.7 2.6
Use unbiased estimation procedures to find point estimates for the following:
a. The population mean
b. The population variance
c. The variance of the sample mean
d. The population proportion of economists predicting growth of at least 2.5% in real gross domestic product |
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| m6771 | A random sample of 10 pairs of identical houses was chosen in a large Midwestern city, and a passive solar heating system was installed in one house from each pair. The total fuel bills (in dollars) for three winter months for these homes were then determined, as shown in the accompanying table. Assuming normal population distributions, find a 90% confidence interval for the difference between the two population means. |
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| m6772 | A random sample of 10 stock market mutual funds was taken. Suppose that rates of returns on the population of all stock market mutual funds follow a normal distribution.
a. The probability is 0.10 that sample variance is greater than what percentage of the population variance?
b. Find any pair of numbers, a and b, to complete the following sentence: The probability is 0.95 that the sample variance is between a% and b% of the population variance.
c. Suppose that a sample of 20 mutual funds had been taken. Without doing the calculations, indicate how this would change your answer to part (b). |
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| m6773 | A random sample of 10 students contains the following observations, in hours, for time spent studying in the week before final exams:
28 57 42 35 61 39 55 46 49 38
Assume that the population distribution is normal.
a. Find the sample mean and standard deviation.
b. Test, at the 5% significance level, the null hypothesis that the population mean is 40 hours against the alternative that it is higher. |
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| m6774 | A random sample of 10 students was asked to rate, in a blind taste test, the quality of two brands of ice cream, one reduced-sugar and one regular ice cream. Ratings were based on a scale of 1 (poor) to 10 (excellent). The accompanying table gives the results. Use the Wilcoxon test to test the null hypothesis that the distribution of the paired differences is centered on 0 against the alternative that the population of all student ice cream consumers prefer the regular brand. |
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| m6775 | A random sample of 100 blue-collar employees at a large corporation are surveyed to assess their attitudes toward a proposed new work schedule. If 60% of all blue-collar employees at this corporation favor the new schedule, what is the probability that fewer than 50 in the random sample will be in favor? |
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| m6776 | A random sample of 100 business majors was asked a series of demographic questions including major, gender, age, year in school, and current grade point average (GPA). Other questions were also asked for their levels of satisfaction with campus parking, campus housing, and campus dining. Responses to these satisfaction questions were measured on a scale from 1 to 5, with 5 being the highest level of satisfaction.
Finally, these students were asked if they planned to attend graduate school within 5 years of their college graduation (0: no; 1: yes). These data are contained in the data file Finstad and Lie Study.
a. Construct a cluster bar chart of the respondents major and gender.
b. Construct a pie chart of their majors. |
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| m6777 | A random sample of 100 measurements of the resistance of electronic components produced in a period of 1 week was taken. The sample skewness was 0.63 and the sample kurtosis was 3.85. Test the null hypothesis that the population distribution is normal. |
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| m6778 | A random sample of 100 men contained 61 in favor of a state constitutional amendment to retard the rate of growth of property taxes. An independent random sample of 100 women contained 54 in favor of this amendment. A confidence interval extending from 0.04 to 0.10 was calculated for the difference between the population proportions. Determine the confidence level of this interval. |
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| m6779 | A random sample of 100 voters is taken to estimate the proportion of a state s electorate in favor of increasing the gasoline tax to provide additional revenue for highway repairs. What is the largest value that the standard error of the sample proportion in favor of this measure can take? |
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| m6780 | A random sample of 104 marketing vice presidents from large Fortune 500 corporations was questioned on future developments in the business environment.
Of those sample members, 50 indicated some measurement of agreement with this statement: Firms will concentrate their efforts more on cash flow than on profits.
What is the lowest level of significance at which the null hypothesis, which states that the true proportion of all such executives who would agree with this statement is one-half, can be rejected against a two-sided alternative? |
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| m6781 | A random sample of 12 college baseball players participated in a special weight-training program in an attempt to improve their batting averages. The program lasted for 20 weeks immediately prior to the start of the baseball season. The average number of weight training hours per week and the change in their batting averages from the preceding season are as follows:
18, 102 120, 1002 15.4, -102 112.4, 792
19.2, 502 115, 892 16, 342 18, 302
118, 682 125, 1102 110, 342 15, 102
Plot the data. Does it appear that the weight-training program was successful? |
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| m6782 | A random sample of 12 college baseball players participated in a special weight-training program in an attempt to improve their batting averages. The program lasted for 20 weeks immediately prior to the start of the baseball season. The average number of hours per week and the change in their batting averages from the preceding season are as follows:
(8.0, 10) (20.0, 100) (5.4, -10) (12.4, 79) (9.2, 50) (15.0, 89) (6.0, 34) (8.0, 30) (18.0, 68) (25.0, 110) (10.0, 34) (5.0, 10)
a. Plot the data. Does it appear that the weight training program was successful?
b. Estimate the regression equation. |
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| m6783 | A random sample of 12 employees in a large manufacturing plant found the following figures for number of hours of overtime worked in the last month:
22 16 28 12 18 36 23 11 41 29 26 31
Use unbiased estimation procedures to find point estimates for the following:
a. The population mean
b. The population variance
c. The variance of the sample mean
d. The population proportion of employees working more than 30 hours of overtime in this plant in the last month |
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| m6784 | A random sample of 12 financial analysts was asked to predict the percentage increases in the prices of two common stocks over the next year. The results obtained are shown in the table. Use the sign test to test the null hypothesis that for the population of analysts there is no overall preference for increases in one stock over the other. |
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| m6785 | A random sample of 120 shoppers was asked to compare two new energy drinks. Sixty-five sample members preferred energy drink A, 53 preferred energy drink B, and 2 expressed no preference. Use the normal approximation to determine if there is an overall preference for either energy drink. |
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| m6786 | A random sample of 125 monthly balances for holders of a particular credit card indicated that the sample skewness was 0.55 and the sample kurtosis was 2.77.
Test the null hypothesis that the population distribution is normal. |
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| m6787 | A random sample of 15 male students and an independent random sample of 15 female students were asked to write essays at the conclusion of a writing course.
These essays were then ranked from 1 (best) to 30 (worst) by a professor. The following rankings resulted: Test the null hypothesis that in the aggregate the two genders are equally ranked against a two-sided alternative. |
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