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1. Determine an appropriate interval width for a random sample of 110 observations that fall between and include each of the following: a.20 to 85 b.30 to 190 c.40 to 230 d.140 to 500
17 62 15 65 28 51 24 65 39 41 35 15 39 32 36 37 40 21 44 37 59 13 44 56 12 54 64 59 a. Construct a frequency distribution. b. Construct a histogram and interpret your result. c. Construct an ogive and interpret your result. d. Construct a stem-and-leaf display and interpret your result. 3. The following table shows the ages of competitors in a charity tennis event in Rome: Age Percent 18–24 18.26 25–34 16.25 35–44 25.88 45–54 19.26 55+ 20.35 a. Construct a relative cumulative frequency distribution. b. What percent of competitors were under the age of 35? c. What percent of competitors were 45 or older?
Class Frequency 0 < 10 8 10 < 20 10 20 < 30 13 30 < 40 12 40 < 50 6 a. Construct a relative frequency distribution. b. Construct a cumulative frequency distribution. c. Construct a cumulative relative frequency distribution and interpret your result. 5. A sample of 20 financial analysts was asked to provide forecasts of earnings per share of a corporation for next year. The results are summarized in the following table: Forecast ($ per share) Number of Analysts 9.95 < 10.45 2 10.45 < 10.95 8 10.95 < 11.45 6 11.45 < 11.95 3 11.95 < 12.45 1 a. Construct the histogram and interpret your result. b. Determine the relative frequencies and interpret your result. c. Determine the cumulative frequencies. d. Determine and interpret the relative cumulative frequencies. 6. The time (in seconds) that a random sample of employees of two companies took to complete a task is:
a. Compute mean, median, and mode for both companies. b. Explain the differences, what do they mean. c. Which measure of central tendency best describes the data? and why? d. Find the standard deviation and coefficient of variation for both and interpret the result economically. e. Compare and comment on standard deviation and coefficient of variation. g. Interpret the results economically. (What does this relation economically mean)
a. Find all three quartiles for both. b. Find Interquartile range for both. c. Find the five-number summary for both . 8. The following data give X, the price charged per piece of table, and Y, the quantity sold (in thousands) Price per Piece (X) Thousands of Pieces Sold (Y) $8 80 9 60
10 50 11 40
12 0 a. Calculate mean, variance and standard deviation for the both variables. b. Compute covariance and correlation coefficient. c. Comment on strength and direction of relationship between the two variables. d. Interpret the results economically. (What does this relation economically mean). e. Comment on strength and direction of relationship between the two variables. 9. A random sample of data has a mean of 75 and a variance of 25. a. Use Chebyshev’s theorem to determine the percent of observations between 65 and 85. b. If the data are mounded, use the empirical rule to find the approximate percent of observations between 65 and 85. 10. Following is a random sample of seven (x, y) pairs of data points: (1,5), (3,7), (4,6), (5,8), (7,9), (3,6), (5,7) a. Compute the covariance. b. Compute the correlation coefficient. 11. Consider the following sample of five values and corresponding weights: xi wi 4.6 8 3.2 3
5.4 6 2.6 2
5.2 5 a. Calculate the arithmetic mean of the xi values without weights. b. Calculate the weighted mean of the xi values. 12. Construct a stem-and-leaf display for the hours that 20 students spent studying for a marketing test. 3.5 2.8 4.5 6.2 4.8 2.3 2.6 3.9 4.4 5.5 5.2 6.7 3.0 2.4 5.0 3.6 2.9 1.0 2.8 3.6
Defect Total Posting error in name 23 Posting error in parcel 21 Property sold after tax bills were mailed 5 Inappropriate call transfer (not part of deeds> 18 mapping) Posting error in legal description>incomplete 4 legal description Deeds received after tax bills printed 6 Correspondence errors 2 Miscellaneous errors 1 a. Construct a Pareto diagram of these defects in data entry and demonstrate your understanding on Pareto diagram. b. What recommendations would you suggest to the county appraiser?
20, 68, 15, 65, 28, 51, 24, 65, 39, 77, 68, 15, 39, 20, 37, 40, 21, 77, 37, 77, 68, 77, 20, 54, 64 a. Determine interval width and boundaries. (number of classes is 5) b. Construct a frequency distribution. c. Draw a histogram d. Draw an Ogive e. Draw a stem-and-leaf display
a. Construct a relative frequency distribution b. Construct a cumulative frequency distribution. c. Construct a cumulative relative frequency distribution. d. Interpret the relative cumulative frequencies.
Defect Code Frequency A 10
B 70 C 15
D 90 E 8
F 4 G 3
accounting class with a stem-and-leaf display. 88 51 63 85 79 65 79 70 73 77
number of 1-gallon bottles of water sold for a random sample of n = 12 hours in one store during hurricane season is: 60 84 65 67 75 72 80 85 63 82 70 75 Describe the central tendency of the data.
the following percentage changes in earnings per share in the current year compared with the previous year: 0% 0% 8.1% 13.6% 19.4% 20.7% 10.0% 14.2%
22. The demand for bottled water increases during the hurricane season in Florida. The number of 1-gallon bottles of water sold for a random sample of n = 12 hours in one store during hurricane season is: 60 84 65 67 75 72 80 85 63 82 70 75 Find the five-number summary.
department about the quality of electrical products sold by the store. Records over a 5-week period show the following number of complaints for each week: 13 15 8 16 8 a. Compute the mean number of weekly complaints. b. Calculate the median number of weekly complaints. c. Find the mode.
stores (CFSs) in an attempt to increase total sales revenue. The daily sales (in hundreds of dollars) from a random sample of 10 weekdays from one of its stores are: 6 8 10 12 14 9 11 7 13 11 a. Find the mean, median and mode for this store. b. Find the five-number summary.
SAT. And suppose the mean score on the mathematics section of the SAT is 570 with a standard deviation of 40. a. Find the z-score for a student who scored 600. b. A student is told that his z-score on this test is -1.5. What was his actual SAT math score?
6 8 7 10 3
Given A = [E1, E3, E7, E9] and B = [E2, E3, E8, E9]. a. What is A intersection B? b. What is the union of A and B? c. Is the union of A and B collectively exhaustive? 27. A corporation takes delivery of some new machinery that must be installed and checked before it becomes available to use. The corporation is sure that it will take no more than 7 days for this installation and check to take place. Let A be the event “it will be more than 4 days before the machinery becomes available” and B be the event “it will be less than 6 days before the machinery becomes available.” a. Describe the event that is the complement of event A. b. Describe the event that is the intersection of events A and B. c. Describe the event that is the union of events A and B. d. Are events A and B mutually exclusive? e. Are events A and B collectively exhaustive? f. Show that (A ᴖ B) ᴗ (Ā ᴖ B) = B.
O1: The Dow Jones average rises on both days. O2: The Dow Jones average rises on the first day but does not rise on the second day. O3: The Dow Jones average does not rise on the first day but rises on the second day. O4: The Dow Jones average does not rise on either day. Let events A and B be the following: A: The Dow Jones average rises on the first day. B: The Dow Jones average rises on the second day. a. Show that (A ᴖ B) ᴗ (Ā ᴖ B) = B. b. Show that A ᴗ (Ā ᴖ B) = A ᴗ B.
a. If the panel reaction is favorable, what is the probabaility that sales will be high? b. If the panel reaction is unforable, what is the probabaility that sales will be low? c. If the panel reaction is neuytral or better, what is the probability that sales will be low?
a. Find the probability of A and B. b. Find the probability of the Complement of A and B. c. Find the probability of union and intersaction of A and B. d. Are the events mutually exlusive? Calculate and explain e. Are the events A and B collectively exhaustive? Calculate and explain
A cell phone company found that 75% of all customers want text messaging on their phones, 80% want photo capability, and 65% want both. What is the probability that a customer will want at least one of these?
In previous example we noted that 75% of the customers want text messaging, 80% want photo capability, and 65% want both. What are the probabilities that a person who wants text messaging also wants photo capability and that a person who wants photo capability also wants text messaging?
Suppose that women obtain 54% of all bachelor’s degrees in a particular country and that 20% of all bachelor’s degrees are in business. Also, 8% of all bachelor’s degrees go to women majoring in business. Are the events “the bachelor’s degree holder is a woman” and “the bachelor’s degree is in business” statistically independent?
AhmedX, a major electronics distributor, has hired Southwest Forecasters, a market research firm, to predict the level of demand (Low (L), Moderate (M) and High (H)) for its new product that combines cell phone and complete Internet capabilities at a price substantially below its major competitors. As part of its deliverables, Southwest provides a rating of Poor (P), Fair (F) or Good(G), on the basis of its research. Prior to engaging Southwest Blue Star, management concluded the following probabilities for the market-demand levels: P(L)=0.5, P(P\L)=0.4, P(P\M)=0.3, P(M)=0.2, P(P\H)=0.5, P(H)=0.6 Using Bayes theorem and probability rules (where needed) find the probability of P (L\P).
before the machinery becomes operational. Number of days 3 4 5 6 7 Probability 0.08 0.24 0.41 0.20 0.07 Let A be the event “it will be more than four days before the machinery becomes operational,” and let B be the event “it will be less than six days before the machinery becomes available.” a. Find the probability of event A. b. Find the probability of event B. c. Are events A and B mutually exclusive? d. Are events A and B collectively exhaustive? e. Find the probability of the intersection of events A and B.
Namin has asked you to determine the return (mean) and risk (standard.deviation) of this portfolio and interpret your results.
 42. Consider the probability distribution function. x 0 1 Probability 0.40 0.60 a. Graph the probability distribution function. b. Calculate and graph the cumulative probability distribution. c. Find the mean of the random variable X. d. Find the variance of X.
Number of returns 0 1 2 3 4 Proportion 0.28 0.36 0.23 0.09 0.04 a. Graph the probability distribution function. b. Calculate and graph the cumulative probability distribution. c. Find the mean of the number of returns of an automobile for corrections for defects during the warranty period. d. Find the variance of the number of returns of an automobile for corrections for defects during the warranty period.
business textbooks is as follows: P(0) = 0.81 P(1) = 0.17 P(2) = 0.02 Find the mean number of errors per page.
Find the expected value and variance for this probability distribution.
estimates that materials will cost $25,000 and that her labor will be $900 per day. If the project takes X days to complete, the total labor cost will be 900X dollars, and the total cost of the project (in dollars) will be as follows: C = 25,000 + 900X Using her experience the contractor forms probabilities (See the table) of likely completion times for the project. COMPLETION TIME x (DAYS) 10 11 12 13 14 Probability 0.1 0.3 0.3 0.2 0.1 a. Find the mean and variance for completion time X. b. Find the mean, variance, and standard deviation for total cost C.
Find the mean and the variance of the distribution.
Assume that these arrivals are independent, with a constant arrival rate, and that this problem follows a Poisson model, with X denoting the number of arriving customers in a 5-minute period and mean l = 2. Find the probability that more than two customers arrive in a 5-minute period. 24. Suppose that Charlotte King has two stocks, A and B. Let X and Y be random variables of possible percent returns (0%, 5%, 10%, and 15%) for each of these two stocks, with the joint probability distribution given in Table 4.7. a. Find the marginal probabilities. b. Determine if X and Y are independent.
Find the mean and variance of the random variable: W = 5X + 4Y 51. A random sample of eight homes in a particular suburb had the following selling prices (in thousands of dollars): 192 183 312 227 309 396 402 390 a. Assume nonnormality and find a point estimate of the population mean that is unbiased and efficient. b. Use an unbiased estimation procedure to find a point estimate of the variance of the sample mean. (Hint: Use sample standard deviation to estimate population standard deviation). c. Use an unbiased estimator to estimate the proportion of homes in this suburb selling for less than $250,000.
X= a. Show that all three estimators are unbiased. b. Which of the estimators is the most efficient? c. Find the relative efficiency of X with respect to each of the other two estimators.
a. The population mean b. The population variance c. The variance of the sample mean d. The population proportion of all mortgages with original purchase price of less than $10,000
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 (n = 12 employees).
a. What is the standard error of the sample mean commuting time? b. What is the probability that the sample mean is fewer than 100 minutes? c. What is the probability that the sample mean is more than 80 minutes? d. What is the probability that the sample mean is outside the range 85 to 95 minutes?
b. 96% confidence level c. 80% confidence level
population variance for the following. a. α = 0.08 b. α /2 = 0.02 58. Assume a normal distribution with known population variance. Calculate the margin of error to estimate the population mean, m, for the following. a. 98% confidence level; n = 64; s2 = 144 b. 99% confidence level; n = 120; s = 100 Calculate the margin of error to estimate the population mean 59. Assume a normal distribution with known population variance. Calculate the width to estimate the population mean, m, for the following. a. 90% confidence level; n = 100; s2 = 169 b. 95% confidence level; n = 120; s = 25 60. Assume a normal distribution with known population variance. Calculate the LCL and UCL for each of the following. a. x = 50; n = 64; σ = 40; a = 0.05 b. x = 85; n = 225; σ2= 400; a = 0.01 c. x = 510; n = 485; σ = 50; a = 0.10 61. It is known that the standard deviation in the volumes of 20-ounce (591-millliliter) bottles of natural spring water bottled by a particular company is 5 millliliters. One hundred bottles are randomly sampled and measured. a. Calculate the standard error of the mean. b. Find the margin of error of a 90% confidence interval estimate for the population mean volume. c. Calculate the LCL, UCL and the width for a 98% confidence interval for the population mean volume. 62. A college admissions officer for an MBA program has determined that historically applicants have undergraduate grade point averages that are normally distributed with standard deviation 0.45. From a random sample of 25 applications from the current year, the sample mean grade point average is 2.90. a. Find a 95% confidence interval for the population mean. b. Based on these sample results, a statistician computes for the population mean a confidence interval extending from 2.81 to 2.99. Find the confidence level associated with this interval.
b. n = 25; 90% confidence level; s2 = 43 64. Calculate the margin of error to estimate the population mean for each of the following (variance is unknown). a. 99% confidence level; x1 = 25; x2 = 30; x3 = 33; x4 = 21 b. 90% confidence level; x1 = 15; x2 = 17; x3 = 13; x4 = 11; x5 = 14 65. Find the LCL and UCL for each of the following. a. α = 0.05; n = 25; x = 560; s = 45 b. . α /2 = 0.05; n = 9; x = 160; s2 = 36 c. 1 - a = 0.98; n = 22; x = 58; s = 15
b. Find the UCL and the LCL of a 90% confidence interval estimate of the mean lifetime of this type of tire if driven under normal driving conditions. 67. Calculate the width for each of the following. a. n = 6; s = 40; . α = 0.05 b. n = 22; s2 = 400; α = 0.01 c. n = 25; s = 50; α = 0.10 68. Find the margin of error to estimate the population proportion for each of the following. a. n = 350; ϸ = 0.30; . α = 0.01 b. n = 275; ϸ = 0.45; . α = 0.05 c. n = 500; ϸ = 0.05; . α = 0.10 69. Calculate the confidence interval to estimate the population proportion for each of the following. a. 98% confidence level; n = 450; ϸ = 0.10 b. 95% confidence level; n = 240; ϸ = 0.01 c. a = 0.04; n = 265; pn = 0.50 70. A business school placement director wants to estimate the mean annual salaries 5 years after students graduate. A random sample of 25 such graduates found a sample mean of $42,740 and a sample standard deviation of $4,780. Find a 90% confidence interval for the population mean, assuming that the population distribution is normal. 71. The production manager of Northern Windows, Inc., has asked you to evaluate a proposed new procedure for producing its Regal line of double-hung windows. The present process has a mean production of 80 units per hour with a population standard deviation of σ= 8. The manager does not want to change to a new procedure unless there is strong evidence that the mean production level is higher with the new process. 72. Demonstrate your understanding on interpretation of the Probability Value, or p-Value. 73. The production manager of Circuits Unlimited has asked for your assistance in analyzing a production process. This process involves drilling holes whose diameters are normally distributed with a population mean of 2 inches and a population standard deviation of 0.06 inch. A random sample of nine measurements had a sample mean of 1.95 inches. Use a significance level of a = 0.05 to determine if the observed sample mean is unusual and, therefore, that the drilling machine should be adjusted. 74. 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 xc 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 75. Demonstrate your understanding on Unbiased Estimator, Most Efficient Estimator and Relative Efficiency Yüklə 103,34 Kb. Dostları ilə paylaş:
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