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| m102745 | The second-leading genetic cause of mental retardation is Fragile X Syndrome, named for the fragile appearance of the tip of the X chromosome in affected individuals. One in 1500 males is affected world-wide, with no ethnic bias.
a. In a sample of 10,000 males, how many would you expect to have Fragile X Syndrome?
b. For a sample of 10,000 males, use the normal approximation to the binomial distribution to determine the probability that more than 7 of the males have Fragile X Syndrome; that at most 10 of the males have Fragile X Syndrome.
c. The probabilities in part (b) were obtained in Exercise 5.109 on page 258 by using the Poisson approximation to the binomial distribution. Which estimates of the true binomial probabilities would you expect to be better, the ones using the normal approximation or those using the Poisson approximation? Explain your answer. |
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| m102746 | The sign test can be used whether or not the variable under consideration has a symmetric distribution. If the distribution is in fact symmetric, the Wilcoxon signed-rank test is preferable. Why do you think that is so? |
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| m102747 | The standard direct labor hours allowed is computed as
a. Unit Labor Standard × Actual Output.
b. Unit Labor Standard × Practical Output.
c. Unit Labor Standard × Standard Output.
d. Unit Labor Standard × Normal Output.
e. Unit Labor Standard × Theoretical Output. |
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| m102748 | The state medical school has discovered a new test for tuberculosis. (If the test indicates a person has tuberculosis, the test is positive.) Experimentation has shown that the probability of a positive test is 0.82, given that a person has tuberculosis. The probability is 0.09 that the test registers positive, given that the person does not have tuberculosis. Assume that in the general population, the probability that a person has tuberculosis is 0.04. What is the probability that a person chosen at random will
(a) Have tuberculosis and have a positive test?
(b) Not have tuberculosis?
(c) Not have tuberculosis and have a positive test? |
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| m102749 | The study "Intrathecal Sufentanil versus Fentanyl for Lower Limb Surgeries - A Randomized Controlled Trial" (Journal of Anaesthesiology Clinical Pharmacology, Vol. 27, Issue 1, pp. 67-73) by P. Motiani et al. compares two different agents, intrathecal sufentail and fentanyl, used in enhancing the anesthesiology of patients receiving major lower limb surgery.One variable compared between the two agents was the amount of blood loss during the surgery. Based on the study, we will assume that, using fentanyl, the amount of blood loss during major lower limb surgery is normally distributed with mean 283.3 ml and standard deviation 83.3 ml. Find the percentage of patients whose amount of blood loss during major lower limb surgery using fentanyl is
a. Less than 304 ml.
b. Between 221 and 429 ml.
c. More than 450 ml. |
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| m102750 | The systolic blood pressure of individuals is thought to be related to both age and weight. For a random sample of 11 men, the following data were obtained:
(a) Generate summary statistics, including the mean and standard deviation of each variable compute the coefficient of variation for each variable. Relative to its mean, which variable has greatest spread of data values? Which variable has the smallest spread of data values relative to its mean?
(b) For each pair of variables, generate the sample correlation coeffi cient r. Compute the corresponding coefficient of determination r2. Which variable (other than x1) has the greatest influence (by itself) on x1? Would you say that both variables x2 and x3 show a strong influence on x1 ? Explain your answer. What percent of the variation in x1 can be explained by the corresponding variation in x2 ? Answer the same question for x3 .
(c) Perform a regression analysis with x1 as the response variable. Use x2 and x3 as explanatory variables. Look at the coeffi cient of multiple determination. What percentage of the variation in x1 can be explained by the corresponding variations in x2 and x3 taken together?
(d) Look at the coeffi cients of the regression equation. Write out the regression equation. Explain how each coeffi cient can be thought of as a slope. If age were held fixed, but a person put on 10 pounds, what would you expect for the corresponding change in systolic blood pressure? If a person kept the same weight b |
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| m102751 | The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.5 minutes and a standard deviation of 2.5 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after another, and that they take off one at a time on a given runway. What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be
(a) Less than 320 minutes?
(b) More than 275 minutes?
(c) Between 275 and 320 minutes? |
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| m102752 | The technology consultancy Data- Genetics published the online document PIN analysis. In addition to analyzing PIN numbers, password trends were examined. Seven million all-numeric passwords were collected and yielded the following estimate of the probability distribution of the number of digits used in an all-numeric password.
a. Explain why the probabilities in the table provide only an estimate of the true probabilities.
b. Estimate the probability that an all-numeric password contains at least six digits. |
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| m102753 | The technology consultancy Data-Genetics published the online document PIN analysis. In addition to analyzing PIN numbers, passwords trends were examined. Seven million all-numeric passwords were collected and yielded the following estimate of the probability distribution of the number of digits used in an all-numeric password.
On average, approximately how many digits would you expect an allnumeric password to have? Explain your answer. |
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| m102754 | The Television Bureau of Advertising publishes a report titled TV Basics for the purpose of providing information to help advertisers make the most effective and efficient use of local and national spot television advertisements. The following table gives a percentage distribution for the location of a television set in the home.
Location ____________________________ Percentage
Living or Sitting Room .............................. 27
Master Bedroom ...................................... 24
Child or other bedroom .............................. 19
Den or Office ......................................... 14
Kitchen or Dining Room ............................ 5
Basement or Garage .................................. 5
Other room or storage ................................. 6
Suppose that a home television set is randomly selected. What is the probability that it is
a. Located in a bedroom?
b. Not located in a bedroom?
c. Located in the kitchen, dining room, basement, or garage? |
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| m102755 | The Times Higher Education "World University Rankings" presents global university performance tables to judge world class universities on the basis of teaching, research, knowledge transfer, and international outlook. The rankings employ 13 carefully calibrated performance indicators to provide comprehensive and balanced comparisons. The top 10 universities for 2012-2013 are as shown in the following table.
What type of data is presented in the
a. First column of the table?
b. Second column of the table?
c. Third column of the table? |
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| m102756 | The Tropical Cyclone Report, a publication of the National Hurricane Center, contains comprehensive information on each tropical cyclone, including synoptic history, meteorological statistics, casualties, and damages. A hurricane is a tropical cyclone with winds that have reached a constant speed of 74 miles per hour or more. During one year, there were 10 Atlantic basin hurricanes. Their maximum wind speeds, in miles per hour (mph), were as shown in the following table.
Consider these storms a population of interest. Obtain the following parameters for the maximum wind speeds. Use the appropriate mathematical notation for the parameters to express your answers.
a. Mean
b. Standard deviation
c. Median
d. Mode
e. IQR |
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| m102757 | The two F-values that divide the area under the curve into a middle 0.95 area and two outside 0.025 areas
Use Table VIII in Appendix A to find the required F-value(s) for an F-curve with df = (4, 8). |
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| m102758 | The two most commonly used scales for measuring temperature are the Fahrenheit and Celsius scales. If you let y denote Fahrenheit temperature and x denote Celsius temperature, you can express the relationship between those two scales with the linear equation y = 32 + 1.8x.
a. Determine b0 and b1.
b. Find the Fahrenheit temperatures corresponding to the Celsius temperatures −40◦, 0◦, 20◦, and 100◦.
c. Graph the linear equation y = 32 + 1.8x, using the four points found in part (b).
d. Apply the graph obtained in part (c) to estimate visually the Fahrenheit temperature corresponding to a Celsius temperature of 28◦. Then calculate that temperature exactly by using the linear equation y = 32 + 1.8x. |
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| m102759 | The United States Office of Personnel Management (OPM) manages the civil service of the federal government. Results from its annual Federal Employee Viewpoint Survey (FEVS) are used to measure employee satisfaction on several work aspects, including Job Satisfaction, Pay Satisfaction, Organization Satisfaction, and an overall measure of satisfaction referred to as Global Satisfaction. In each case a 100-point scale with higher values indicating greater satisfaction is used (OPM website, July 6, 2016). Scores for Global Satisfaction, Job Satisfaction, Pay Satisfaction, and Organization Satisfaction for a sample of 65 employees are provided in the DATAfile named Satisfaction.
a. Develop the estimated multiple regression equation that can be used to predict the Global Satisfaction score using the Job Satisfaction, Pay Satisfaction, and Organization Satisfaction scores.
b. Predict the overall Global Satisfaction score for an employee with a Job Satisfaction score of 72, a Pay Satisfaction score of 54, and an Organization Satisfaction score of 53. |
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| m102760 | The United States ranks ninth in the world in per capita chocolate consumption; the average American eats 9.5 pounds of chocolate annually (Forbes, July 22, 2015). Suppose you are curious whether chocolate consumption is higher in Hershey, Pennsylvania, the location of The Hershey Company s corporate headquarters. A sample of 36 individuals from the Hershey area showed a sample mean annual consumption of 10.05 pounds and a standard deviation of s - 1.5 pounds. Using α =.05, do the sample results support the conclusion that mean annual consumption of chocolate is higher in Hershey than it is throughout the United States? |
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| m102761 | The U.S. Census Bureau collects information about the ages of people in the United States. Results are published in Current Population Reports. a. Identify the variable and population under consideration.
b. A sample of six U.S. residents yielded the following data on ages (in years). Determine the median of these age data. Decide whether this descriptive measure is a parameter or a statistic, and use statistical notation to express the result.
c. By consulting the most recent census data, we found that the median age of all U.S. residents is 37.2 years. Decide whether that descriptive measure is a parameter or a statistic, and use statistical notation to express the result. |
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| m102762 | The U.S. Census Bureau collects information on the U.S. population by ancestry and region of residence and publishes the results in American Community Survey. According to that document, 18% of the population resides in the Northeast.
a. If ancestry and region of residence are not associated, what percentage of Americans of Irish ancestry would reside in the Northeast?
b. There are roughly 37 million Americans of Irish ancestry. If ancestry and region of residence are not associated, how many Americans of Irish ancestry would reside in the Northeast?
c. There are, in fact, 9.25 million Americans of Irish ancestry who reside in the Northeast. Given this information and your answer to part (b), what can you conclude? |
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| m102763 | The U.S. Census Bureau compiles census data on educational attainment of Americans. From the document Current Population Survey, we obtained the 2010 distribution of educational attainment for U.S. adults 25 years old and older. Here is that distribution.
Highest level Percentage
Not HS graduate........................12.9
HS graduate..............................31.2
Some college.............................16.8
Associate s degree........................9.1
Bachelor s degree.......................19.5
Advanced degree.......................10.5
A random sample of 500 U.S. adults (25 years old and older) taken this year gave the following frequency distribution.
Highest level Frequency
Not HS graduate..................45
HS graduate.....................163
Some college........................76
Associate s degree...............53
Bachelor s degree...............102
Advanced degree................61
Decide, at the 5% significance level, whether this year s distribution of educational attainment differs from the 2010 distribution. |
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| m102764 | The U.S. Census Bureau compiles information on money income of people by type of residence and publishes its finding in Current Population Reports. Independent simple random samples of people residing inside principal cities (IPC), outside principal cities but within metropolitan areas (OPC), and outside metropolitan areas (OMA), gave the following data on income level.
a. Identify the populations under consideration.
b. Identify the variable under consideration.
c. At the 5% significance level, do the data provide sufficient evidence to conclude that people residing in the three types of residence are nonhomogeneous with respect to income level? |
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