Using And Interpreting Statistics 3rd Edition Eric W. Corty - Solutions

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Problem 2.20 Two digits are chosen without replacement from the set of integers {1, 2, 3, 4, 5, 6}. Let Ai, i = 3, 4,..., 11 denote the event that the sum of the integers chosen equals i. Compute P(Ai), i = 3, 4,..., 11.
Problem 2.19 Two digits are chosen without replacement from the set of integers {1, 2, 3, 4, 5}. (a) Describe the sample space and assign to each sample point the equally likely probability measure. (b) What is the probability that both digits are less than or equal to 3? (c) What is the
Problem 2.18 Compute n k for: (a) n = 10, k = 0, 1, 2, 3 (b) n = 10, k = 7, 8, 9, 10 (c) n = 12, k = 10, 11, 12 (d) n = 12, k = 0, 1, 2
Problem 2.17 (a) Compute P10,k for k = 1, 2, 3. (b) Given that P9,3 = 504, compute P9,k for k = 4, 5, 6.
Problem 2.16 How many k-strings (words of length k) from the finite set S = {1, 2, 3, 4, 5} are there for: (a) k = 1? (b) k = 2? (c) k = 3?
Problem 2.15 Let B denote an event for which P(B) > 0. Define a set function P via the recipe P (A) = P(A ∩ B) P(B) . Show that P satisfies the axioms for a probability measure. P (A) is called “the conditional probability of A given that B has occurred.” Section 2.3: Discrete sample
Problem 2.14 Suppose P(A) = 0.7, P(B) = 0.8. Show that P(An B) > 0.5.
Problem 2.13 Which of the following statements are true? false? (a) ACB then P(B) P(A) (b) P(A) = P(B) then A = B (c) P(An B) = 0 then either P(A) = 0 or P(B) = 0
Problem 2.12 Given P(A1)=0.5, P(A2)=0.4, P(A3)=0.4, P(A1 ∩ A2) = .04, P(A1 ∩ A3)=0.1, P(A2 ∩ A3)=0.2, P(A1 ∩ A2 ∩ A3)=0.02. Using this information, Venn diagrams, and Propositions 2.1 and 2.5 compute the following probabilities: (a) P(A1 ∪ A2 ∪ A3) (b) P(A 1 ∩ A 2 ∩ A 3) (c)
Problem 2.11 A and B are events whose probabilities are given by P(A)=0.7, P(B)=0.4, P(A ∩ B)=0.2. Compute the following probabilities: (a) P(A ∪ B) (b) P(A ∩ B ) (c) P(A ∪ B ) (d) P(A ∩ B) (e) P(A ∩ B ) (f) P(A ∪ B) (g) P(A ∪ B )
Problem 2.10 Compute the probabilities of each of the events in the previous problem; assume all sample points have the same probability 1/36.
Problem 2.9 Let S denote the sample space for the game of craps (described in Table 2.1) and let Ai denote the events defined in Table 2.2. Express each of the following events in terms of the events Ai. (a) An odd number is thrown. (b) A number ≤ 6 is thrown (c) A number > 6 is thrown.
Problem 2.8 Let Wi, i = 1, 2, 3 denote the event that component i is working. W i denotes the event that the ith component is not working. Express in set theoretic language the following events: Of the components W1, W2, W3 (a) only W1 is working (b) all three components are working (c) none are
Problem 2.7 In the paper The Significant Digit Phenomenon, American Mathematical Monthly, Vol. 102, No. 4, April 1995, the author proposes the following probability distribution for the first significant digit: P(sd) = log10 1 + 1 d , d = 1, 2,..., 9. Here, sd is the event that the first
Problem 2.6 In an environmental study of the effect of radon gas on a population, blood samples were drawn from human volunteers, 100 cells were cultured and the number of cells that exhibited chromosome aberrations were counted. Denote by si the event that i chromosome aberrations occurred. Based
Problem 2.5 A quality control engineer observes that a printed circuit board with i defects (i = 0, 1, 2, 3, 4) seems to occur with a frequency inversely proportional to i + 1; that is, the sample space corresponding to this experiment consists of the finite set of points S = {s0, s1, s2, s3, s4},
Problem 2.4 Refer to the sample space of Example 2.1 displayed in Table 2.1. (a) List all sample points in the event A = {both faces are odd}. (b) List all sample points in the event A . (c) Let B = {an even number is thrown}. Show that A ⊂ B. (d) Describe, in plain English, the event A ∩ B.
Problem 2.3 This is a continuation of Problem 2.1. Express in terms of the sets Ai, Bi defined above the following events: (a) No more than two tails were thrown. (b) Exactly three tails were thrown. (c) No tails were thrown. (d) Only tails were thrown.
Problem 2.2 This is a continuation of Problem 2.1. Which of the following statements are true? false? (a) A 0 = B1 (b) B2 = A2 ∪ A3 ∪ A4 (c) B2 ⊂ A2 (d) A2 ⊂ B2
Problem 2.1 The sample space corresponding to the experiment of tossing a coin 4 times is listed below. Assume all 16 sample points have equal probabilities. HHHH THHH HHHT THHT HHTH THTH HHTT THTT HTHH TTHH HTHT TTHT HTTH TTTH HTTT TTTT Let Ai and Bi denote, respectively, the events “exactly i
Problem 1.83 Refer to the weekly 2002 return data for PTTRX listed in Table 1.20, Section 1.11. Use a statistical software package to: (a) Draw the scatter plot of PTTRX returns (y) against the S&P returns (x), and compute the correlation coefficient. (b) Compute PTTRX’s beta for the year 2002.
Problem 1.82 Refer to the weekly 2002 return data for GE listed in Table 1.20, Section 1.11. Use a statistical software package to: (a) Draw the scatter plot of GE returns (y) against the S&P returns (x) and compute the correlation coefficient. Compare this scatter plot to the one in Figure 1.18
Problem 1.81 Sir Francis Galton (1822–1911), author of Hereditary Genius (1869) and a cousin of Charles Darwin (1809–1882), was interested in finding scientific laws governing the inheritance of physical traits. He was particularly interested in how the heights of parents were passed on to
Problem 1.80 Refer to the StatLab data set (Table 1.16). (a) Draw the scatter plot of mother’s weight (y) vs. mother’s height (x). (b) Compute the sample correlation r.
Problem 1.79 Refer to the fuel efficiency data set of Problem 1.76. (a) Draw the scatter plot of gpm (y) vs. engine displacement (x). (b) Calculate the least squares estimates b0 and b1 and draw the graph of the regression line y = b0 + b1x. Use the same axes on which you graphed the scatter plot.
Problem 1.78 Refer to the fuel efficiency data set of Problem 1.76. (a) Draw the scatter plot of mpg (y) vs. engine displacement (x). (b) Calculate the least squares estimates b0 and b1 and draw the graph of the regression line y = b0 + b1x. Use the same axes on which you graphed the scatter plot.
Problem 1.77 Refer to the fuel efficiency data set of the previous Problem 1.76. (a) Draw the scatter plot of gpm (y) vs. car weight (x). (b) Calculate the least squares estimates b0 and b1 and draw the graph of the regression line y = b0 + b1x. Use the same axes on which you graphed the scatter
Problem 1.76 The table below records the curbside weight (in units of 1000 lbs), fuel consumption in miles per gallon (mpg), engine displacement (disp), and fuel consumption in gallons per 100 miles (gpm) for 18 2004-05 model year automobiles. (Displacement is a measure of the size, in liters, of
Problem 1.75 The following data record the amount of water (x), in centimeters, and the yield of hay (y), in metric tons per hectare, on an experimental farm. water (x) 30 45 60 75 90 105 120 yield (y) 2.11 2.27 2.5 2.88 3.21 3.48 3.37 (a) Draw the scatter plot (xi, yi). (b) Calculate the least
Problem 1.74 The two columns of data in the table below are the living area X (in square feet) and the selling price $Y (in thousands of dollars) of 12 residential properties. Area(sq.feet) Price(thousands of dollars) 1360 78.5 1940 175.7 1750 139.5 1550 129.8 1790 95.6 1750 110.3 2230 260.5 1600
Problem 1.73 Suppose the data set Y = {y1,...,yn} is obtained from X = {x1,...,xn} by means of the linear transformation yi = axi +b, wherea, b are constants and a > 0. (a) Show that the order statistics for the data set Y are given by y(i) = ax(i) +b. (b) Let Qx(p) and Qy(p) denote the quantiles
Problem 1.72 35 items were inspected and the number of defects per item were recorded: 2301000 0023313 3100200 2120103 1400104 (a) Compute the mean and median number of defects per item. (b) Compare the mean and median and explain why they differ.
Problem 1.71 The following data comes from an experiment that measures the weight loss for a group of 30 men who have been randomly assigned to three different weight loss programs labeled A, B, C, respectively. AB C ABC 15.3 3.4 11.9 10 5.2 8.8 2.1 10.9 13.1 8.3 2.5 12.5 8.8 2.8 11.6 9.4 10.5 8.6
Problem 1.70 Suppose each observation xi is bounded above and below by M, m, respectively; that is, assume that m ≤ xi ≤ M, i = 1, . . . n. (a) Show that m ≤ x ≤ M. (b) The writer Garrison Keillor has described the mythical town of Lake Wobegon as a place “where all the women are strong,
Problem 1.69 (a) Carefully plot the following risky portfolios on the graph below, with risk s plotted on the x axis and mean return r on the y axis. Portfolio A B C D E F G H risk s 23 21 25 29 29 32 35 45 mean return r 10 12.5 15 16 17 18 18 20(b) Referring to the graph you constructed in part
Problem 1.68 Refer to the weekly 2002 return data for BEARX listed in Table 1.20, Section 1.11. Use a statistical software package to compute: (a) the sample mean of the 2002 BEARX returns. (b) the sample standard deviation of the 2002 BEARX returns. (c) Compare these results to the mean and
Problem 1.65 Compute the sample mean, sample variance and sample standard deviation for the cadmium levels displayed in Problem 1.19. Problem 1.66 Refer to the weekly 2002 return data for GE listed in Table 1.20, Section 1.11. Use a statistical software package to compute: (a) the sample mean of
Problem 1.64 The following data give the results of an experiment to study the effect of two different word processing programs on the length of time (measured in minutes) to type a text file. A group of 16 were randomly divided into 2 groups of 8 secretaries each, and each group was randomly
Problem 1.63 Refer to the dopamine b-hydroxylase (DBH) activity data set of Problem 1.40. (a) Compute the sample mean and sample standard deviation of the DBH activity for the non-psychotic group. (b) Compute the sample mean and sample standard deviation of the DBH activity for the psychotic group.
Problem 1.62 The following table gives the concentration of thiol in lysate in the blood of two groups: a “normal” group and a group suffering from rheumatoid arthritis.Data Analysis 59 Thiol Concentration Normal Rheumatoid 1.84 2.81 1.92 4.06 1.94 3.62 1.92 3.27 1.85 3.27 1.91 3.76 2.07
Problem 1.61 The data in Problem 1.18 come from an experiment where the goal is to control all the factors except the one we are testing. The factors of age and neighborhood were controlled by pairing the children of the same age and neighborhood; they differed with respect to their parents’
Problem 1.60 Refer to the data in Problem 1.18. (a) Compare the lead levels in the blood of the exposed and control groups of children by computing the sample mean, sample variance and sample standard deviation of the amount of lead in the blood of both groups. (b) What inferences can you draw from
Problem 1.59 Compute the sample mean, sample variance and sample standard deviation for the capacitances listed in Problem 1.20.
Problem 1.58 Refer to the reverse–bias collector current of Problem 1.28. Compute the sample mean and sample standard deviation.
Problem 1.57 Refer to the battery data of Problem 1.5. Compute the sample mean and sample standard deviation.
Problem 1.56 With reference to the failure times of the air conditioning systems in Problem 1.37 find the sample means, variances and standard deviations of: (a) Airplane B7912 (b) Airplane B7913 (c) Airplane B7914 (d) Airplane B8045 (e) How do you explain the fact that in each of the above cases
Problem 1.55 Refer to the infant weight gain data in Example 1.7 (Table 1.6). (a) Compute the sample mean, sample variance and sample standard deviation of the infant weight gain for smoking mothers. (b) Compute the sample mean, sample variance and sample standard deviation of the infant weight
Problem 1.54 Refer to the breast-milk volume data in Example 1.7 (Table 1.6). (a) Compute the sample mean, sample variance, and sample standard deviation of the milk volume for smoking mothers. (b) Compute the sample mean, sample variance, and sample standard deviation for nonsmoking mothers. (c)
Problem 1.53 Find the sample means, variances, and standard deviations of the bearing lifetimes of Problem 1.27.
Problem 1.52 The frequency distribution for girls’ scores on an achievement test is given in the table below. Key to the table: Score = x and Freq = f(x). SCORE 14 15 19 20 21 24 25 27 28 29 31 32 FREQ 111111311312 SCORE 33 34 35 36 37 38 39 40 42 43 45 FREQ 13312312111 Compute the sample mean
Problem 1.51 The frequency distribution for the heights of 36 adult males is given in the table below. Key to the table: Height = x and Freq = f(x). HEIGHT 64.9 65 65.5 66 67 67.8 68 68.1 68.5 69 70 FREQ 1 2 1 1 1 1 1 1 1 3 3 HEIGHT 70.1 70.5 70.8 71 71.8 72 72.8 73 73.5 74 75 Freq 1 1 1 6 1 2 1 1
Problem 1.50 Refer to the DNA damage data given in Table 1.7. (a) Compute the sample mean, sample variance, and sample standard deviation for the N1-THB-ADE levels for the exposed workers. (b) Compute the sample mean, sample variance, and sample standard deviation for the N1-THB-ADE levels for
Problem 1.49 One measure of the effect of sewage effluent on a lake is to determine the concentration of nitrates in the water. Assume that the following data, which are simulated, were obtained by taking 12 samples of water, dividing each sample into two equal parts and measuring the nitrate
Problem 1.48 Find the sample means, variances and standard deviations of the burst strengths of a rocket motor listed in Problem 1.7.
Problem 1.47 Find the sample means, variances and standard deviations of the lifetimes of the type B filaments in Table 1.5.
Problem 1.46 Eleven samples of the outflow from a sewage treatment plant were divided in two parts with one half going to a commercial laboratory (columns 1 and 2) and the other half sent to a state laboratory (columns 3 and 4). Each laboratory measured the biochemical oxygen demand (BOD) and the
Problem 1.45 Refer to the Benzo(a)pyrene levels of Problem 1.6. Compute (two decimal place accuracy): the sample mean, sample variance, and sample standard deviation.
Problem 1.44 Refer to the ozone level data of Problem 1.21. Compute the sample mean, sample variance and standard deviation of the ozone levels.
Problem 1.43 Refer to Lord Rayleigh’s data in Table 1.4. Compute: (a) The sample mean and standard deviation of the mass of nitrogen obtained from air. (b) The sample mean and standard deviation of the mass of nitrogen obtained by chemical decomposition.
Problem 1.42 The analytical methods committee of the Royal Society of Chemistry reported the following results on the determination of tin in foodstuffs. The samples were boiled with hydrochloric acid under reflux for different times. Refluxing time (min) Tin found (mg/kg) 30 55 57 59 56 56 59 75
Problem 1.41 The manufacturer’s cost and the selling price (in dollars) of light bulbs are denoted by C1, C2, respectively. The bulb is guaranteed for H hours; if the bulb fails before then the manufacturer guarantees a total refund. Let R denote the manufacturer’s net revenue. Using the type A
Problem 1.40 The following data gives the results of a study of 25 hospitalized schizophrenic patients who were treated with anti-psychotic medication, and after a period of time were classified as psychotic or non-psychotic by hospital staff. Samples of cerebrospinal fluid were taken from each
Problem 1.39 Refer to the capacitances data in Problem 1.20. (a) Compute the median, the lower and upper quartiles, and the IQR; are there any outliers? (b) Draw the box plot.
Problem 1.38 Refer to the data on lead absorption in children of employees who worked in a factory where lead is used to make batteries (see Problem 1.18). Compare the exposed group with the control group by drawing the box plot for the difference variable di = xi − yi, (i = 1,..., 33). What
Problem 1.37 The times between successive failures of the air conditioning system of Boeing 720 jet airplanes is shown in the table below. It contains 97 values taken from 4 airplanes. This is an edited version of the original data set which contained the maintenance data on a fleet of 13
Problem 1.36 Refer to the failure times data of Table 1.21. (a) Compute the safe life Q(0.10). (b) Compute the sample range and the IQR. (c) Identify all outliers. (d) Draw the box plot.
Problem 1.35 Refer to the DNA damage data given in Table 1.7. (a) Compute the median x˜, Q1, Q3, and IQR for the N-1-THB-ADE levels for the exposed workers. Identify all outliers, if any. (b) Compute the median x˜, Q1, Q3, and IQR for the N-1-THB-ADE levels for the control group of workers.
Problem 1.34 Refer to the infant weight gain data in Example 1.7 (Table 1.6). (a) Compute the median x˜, Q1, Q3, and IQR of the infant weight gain for the smoking mothers data. Identify all outliers, if any. (b) Compute the median, Q1, Q3, and IQR of the infant weight gain for the non-smoking
Problem 1.33 Refer to the breast-milk volume data in Example 1.7 (Table 1.6). (a) Compute the median x˜, Q1, Q3, and IQR for the smoking mothers data. Identify all outliers, if any. (b) Compute the median, Q1, Q3, and IQR for the non-smoking mothers data. Identify all outliers, if any. (c) Draw
Problem 1.32 Refer to the lifetimes of type A and type B filaments listed Table 1.5. Draw the side-by-side box plots of the two filament types. Using this information compare the lifetimes and variability of the type A and type B filaments.
Problem 1.31 Refer to the battery data of Problem 1.5. (a) Compute the sample range, median, Q1, Q3 and the IQR. (b) Draw the box plot.
Problem 1.30 Show that the ith order statistic x(i) is the (i − 0.5)/n quantile by deriving Equation 1.17.
Problem 1.29 In Example 1.20 we used the graph of the empirical distribution function (Figure 1.12) to compute the median of the radiation data (Table 1.3). (a) Use the same graphical method to compute the lower and upper quartiles. (b) Compute the lower and upper quartiles using Equation 1.16.
Problem 1.28 The following data record the reverse–bias collector current (in micro-amperes) for a set of twenty transistors. Reverse–bias collector current (in micro-amperes) for a set of n = 20 transistors 0.20 0.16 0.20 0.48 0.92 0.33 0.20 0.53 0.42 0.50 0.19 0.22 0.18 0.17 1.20 0.14 0.09
Problem 1.27 The lifetimes (in hours) of 20 bearings are recorded in the following table. 6278 3113 9350 5236 11584 12628 7725 8604 14266 6215 3212 9003 3523 12888 9460 13431 17809 2812 11825 2398 (Source: R. E. Schafer and J. E. Angus (1979), Estimation of Weibull Quantiles With Minimum Error in
Problem 1.25 Refer to the lifetimes of type B filaments in Table 1.5. (a) Compute the sample range and median of the lifetimes. (b) Compute the lower and upper quartiles and the IQR. Are there any outliers?Problem 1.26 The annual income (in thousands of dollars) of 30 families in a metropolitan
Problem 1.23 Refer to the Benzo(a)pyrene levels of Problem 1.6. Compute: (a) the sample median. (b) the upper and lower quartiles and the IQR (inter quartile range). (c) Draw the boxplot and identify the outliers if there be any.Problem 1.24 The 1989 total charges (in dollars) for 33 female
Problem 1.22 Let Fˆ(x) be the empirical distribution function for the ozone data of Problem 1.21. Compute the empirical distribution function Fˆ(x) for the following x values: (a) Fˆ(4.5) (b) Fˆ(5.2) (c) Fˆ(5.6) (d) Fˆ(1.1) (e) Fˆ(6.9)
Problem 1.21 The following data record ten measurements of the ozone concentration (in ppm) in downtown Los Angeles. {4.0, 1.9, 7.1, 4.7, 4.9, 5.8, 6.1, 6.1, 7.3, 3.0}. Compute (two decimal place accuracy): (a) the order statistics. (b) the sample median. (c) the upper and lower quartiles and the
Problem 1.20 The following table records the measured capacitances of 40 capacitors rated at 0.5 micro farads (µ(F)). 0.5121 0.5059 0.4838 0.4981 0.4851 0.4964 0.4955 0.4990 0.5092 0.5075 0.4905 0.5026 0.5010 0.4863 0.5100 0.5042 0.4944 0.5084 0.5031 0.5072 0.5170 0.4957 0.5056 0.5038 0.5066
Problem 1.19 Cadmium (Cd) is a bluish–white metal used as a protective coating for iron, steel and copper. Overexposure to cadmium dust can damage the lungs, kidney and liver. The federal standard for cadmium dust in the workplace is 200µg/m3. The following (simulated) data was obtained by
Problem 1.18 The following table records the results of a study of lead absorption in children of employees who worked in a factory where lead is used to make batteries. In this study the authors matched 33 such children (exposed) from different families to 33 children (control) of the same age
Problem 1.17 Carbon dioxide (CO2) emissions are believed to be associated with the phenomenon of global warming. The following data come from a sample of the twenty countries with the highest CO2 emissions in 1989. Key to the variables: The four variables are: X1 = 1989 emissions, X2 = 1989
Problem 1.16 Refer to the weekly 2002 return data for BEARX listed in Table 1.20. Use a statistical software package to: (a) Draw the time series plot of the weekly returns of BEARX stock. Is there any pattern in this time series that an investor can take advantage of ? (b) Draw the frequency
Problem 1.15 Refer to the weekly 2002 price and return data for PTTRX listed in Tables 1.18 and 1.20. Use a statistical software package to: (a) Draw the time series plot of the weekly returns of PTTRX mutual fund. Is there any pattern in this time series that an investor can take advantage of ?
Problem 1.14 Refer to the weekly 2002 price and return data for GE listed in Tables 1.18 and 1.20. Use a statistical software package to: (a) Draw the time series plot of the weekly returns of GE stock. Is there any pattern in this time series that an investor can take advantage of ? (b) Draw the
Problem 1.13 Refer to the weekly 1999 return data for BEARX listed in Table 1.19. (a) Draw the frequency histogram of the weekly returns and comment on its shape. Is it symmetric? skewed left? skewed right? (b) Comment on the similarities and differences between the histogram obtained in part (a)
Problem 1.12 Refer to the weekly 1999 return data for PTTRX listed in Table 1.19. (a) Draw the frequency histogram of the weekly returns and comment on its shape. Is it symmetric? skewed left? skewed right? (b) Comment on the similarities and differences between the histogram obtained in part (a)
Problem 1.11 Refer to the weekly 1999 return data for GE listed in Table 1.19. (a) Draw the frequency histogram of the weekly returns and comment on its shape. Is it symmetric? skewed left? skewed right? (b) Comment on the similarities and differences between the histogram obtained in part (a) and
Problem 1.10 An important performance measure of a stock market portfolio is to compute its annualized returns for the best three-year period, as well as the worst three-year period, over the past ten years. For the S&P500 the best three-year period (over the 10-year period 1995-2004) is
Problem 1.9 An International Equity Fund reported the annual returns for the years 2001- 2005 in the following table. year 2001 2002 2003 2004 2005 returns -9.04% -8.25% 26.13% 22.94% 11.55% (a) At the beginning of 2001 Ms. Allen invests $10,000 in this mutual fund where it remains for the next
Problem 1.8 The following table lists 24 measurements (psi) of the operating pressure of a rocket motor. 7.7401 7.7749 7.7227 7.77925 7.96195 7.4472 8.0707 7.89525 8.0736 7.4965 7.5719 7.7981 7.8764 8.1925 8.01705 7.9431 7.71835 7.87785 7.2904 7.7575 7.3196 7.6357 8.06055 7.9112 (Source: I. Guttman
Problem 1.7 The following table lists 17 measurements of the burst strength of a rocket motor chamber. 15.30 17.10 16.30 16.05 16.75 16.60 17.10 17.50 16.10 16.10 16.00 16.75 17.50 16.50 16.40 16.00 16.20 (Source: S. Weerahandi & R. A. Johnson (1992), Testing Reliability in a Stress–Strength
Problem 1.6 The following data record 14 measurements of the air concentration (measured in µ/gm3) of Benzo(a)pyrene (BAP) in a house located near a metal pipe foundry.Introduction to Probability and Statistics for Science, Engineering, and Finance 10 10 25 40 40 45 45 55 55 70 75 90 220 285 Let
Problem 1.5 The following data are the measurements of the capacity (in ampere-hours) of 10 batteries. {157, 152, 146, 153, 151, 154, 149, 148, 153, 147} (a) Compute the order statistics. (b) Compute the empirical distribution function Fˆn(x) for x = 145, 150, 150.5, 152.9, 153.1, 158. (c) Graph
Problem 1.4 Refer to the lifetimes of type B filaments in Table 1.5; compute: (a) the order statistics; (b) the cumulative frequency distribution F(x) for: x = 1065, 1100, 1143. (c) Graph the empirical distribution function Fˆn(x).
Problem 1.3 Refer to the radiation data through the open door in Problem 1.1. To obtain a data set with a more symmetric distribution Johnson and Wichern used the same function as in Problem 1.2; that is, the transformed data is given by yi = x0.25 i − 1 0.25 . The transformed data set is shown
Problem 1.2 Statisticians prefer to work with distributions that are symmetrically distributed about a single well-defined peak. When the data are skewed, as is the case for the radiation data (see Figure 1.10), the statisticians Box and Cox have shown that transforming the data by means of the
Problem 1.1 The manufacturer of microwave ovens (see Example 1.4) also measured the radiation emitted through the open doors of the 42 microwave ovens and recorded the emitted radiation in the table below. 0.30 0.09 0.30 0.10 0.10 0.12 0.09 0.10 0.09 0.10 0.07 0.05 0.01 0.45 0.12 0.20 0.04 0.10
A sleep specialist believes that the more caffeine a person consumes per day, the more episodes of restless sleep that person experiences. What are her null and alternative hypotheses?

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