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mathematics
statistics

Questions and Answers of Statistics

Use the following listed chest deceleration measurements from samples of small, midsize, and large cars. Use a 0.05 significance level to test the claim that the different size categories have the
Listed below are highway fuel consumption amounts (mi/gal) for cars categorized by the sizes of small, midsize, and large (from Data Set 14 in Appendix B). Using a 0.05 significance level, test the
Data Set 5 in Appendix B lists performance IQ scores for random samples of subjects with blood lead levels categorized as low, medium, and high. Use a 0.01 significance level to test the claim that
Data Set 9 in Appendix B lists measured cotinine levels from a sample of subjects who smoke, another sample of subjects who do not smoke but are exposed to environmental tobacco smoke, and a third
Refer to Data Set 10 in Appendix B and use the amounts of nicotine (mg per cigarette) in the king-size cigarettes, the 100-mm menthol cigarettes, and the 100-mm nonmenthol cigarettes. The king-size
Refer to Data Set 13 in Appendix B and use the pelvis decel-eration measurements for small cars, midsize cars, and large cars. Use a 0.05 significance level to test the claim that the different size
In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H byFor each individual group of tied observations in the combined set of
If the methods of this section are used with paired sample data, and the conclusion is that there is sufficient evidence to support the claim of a correlation between the two variables, can we use
What do r, rs p, and ps denote? Why is the subscript s used? Does the subscript s represent the same standard deviation s introduced in Section 3-3?
Refer to Table 13-2 in Section 13-1 and identify the efficiency of the rank cor-relation test. What does that value tell us about the test?
Use the scatterplot to find the value of the rank correlation coefficient rs and the critical values corresponding to a 0.05 significance level used to test the null hypothesis of ps = 0. Determine
Use the scatterplot to find the value of the rank correlation coefficient rs and the critical values corresponding to a 0.05 significance level used to test the null hypothesis of ps = 0. Determine
The following table lists overall quality scores and prices of 40-inch LCD televisions. Do these data suggest that you can get better quality by spending more?Use the rank correlation coefficient to
The following table lists overall qual¬ity scores and prices for a gallon of exterior paints. Do these data suggest that you can get better quality by spending more?Use the rank correlation
Two judges ranked seven bands in the Texas state finals competition of marching bands (Coppell, Keller, Grapevine, Dickinson, Poteet, Fossil Ridge, Heritage), and their rankings are listed below.
In the same competition described in Exercise 9, a third judge ranked the bands with the results shown below. Test for a correlation between the first and third judges. Do the judges appear to rank
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights of the seals (in kg). The data are based on €œMass Estimation of Weddell Seals Using Techniques of
The association between the temperature and the number of times a cricket chirps in 1 min was studied. Listed below are the numbers of chirps in 1 min and the corresponding temperatures in degrees
Refer to the measured systolic and diastolic blood pressure measure¬ments of 40 randomly selected males in Data Set 1 in Appendix B and test the claim that among men, there is a correlation between
Refer to Data Set 6 in Appendix B and use the paired data con¬sisting of brain volume (cm3) and IQ score. Use the data from Appendix B to testfor rank correlation with a 0.05 significance level.
Refer to Data Set 15 in Appendix B and use the departure delay times and the arrival delay times. Use the data from Appendix B to testfor rank correlation with a 0.05 significance level.
Refer to Data Set 16 in Appendix B and use the magnitudes and depths from the earthquakes. Use the data from Appendix B to testfor rank correlation with a 0.05 significance level.
An alternative to using Table A-9 to find critical values for rank correlation is to compute them using this approximation:
The last 106 baseball seasons ended with 62 World Series wins by American League teams and 44 wins by National League teams. Can the runs test be used to show that the American League is better
If we use a 0.05 significance level to test for randomness of the sequence given in Exercise 2, we conclude that there is not sufficient evidence to reject randomness.a. Rearrange the sequence so
The political parties of the winning candidates for a recent sequence of presidential elections are listed below.€ƒD denotes Democratic party and R denotes Republican party. Does it appear that we
New York Times article about the calculation of decimal places of it noted that €œmathematicians are pretty sure that the digits of tt are indistinguish¬able from any random
In 1970, a lottery was used to determine who would be drafted into the U.S.Army. The 366 dates in the year were placed in individual capsules, they were mixed, then cap¬sules were selected to
Media experts claim that daily newspapers are declining because of Internet access. Listed below are the numbers of daily newspapers in the United States for a recent se¬quence of 20 years. Shown
Listed below are the conference designations of teams that won the Super Bowl, where N denotes a team from the NFC and A denotes a team from the AFC. Do the results suggest that either conference is
Test the claim that the sequence of World Series wins by American League and National League teams is random. Given below are recent results (as of this writing), with American League and National
Listed below are the annual high values of the Dow Jones Industrial Average for a recent sequence of years (as of this writing). Test for randomness below and above the median. What does the result
Listed below are global mean temperatures (°C) of the earth for 50 re¬cent and consecutive years (based on data from the Goddard Institute for Space Studies). Test for randomness above and
a. Find the number of runs for each of the 84 sequences.b. Use the results from parts (a) and (b) to find your own critical values for G.c. Compare your results to those given in Table A-10.
The last 106 baseball seasons (as of this writing) ended with 62 World Series wins by American League teams, compared to 44 wins by National League teams. Use the sign test with a 0.05 significance
Listed below are the costs (in dollars) of flights from New York (JFK) to San Francisco for US Air, Virgin America, Delta, American, Continental, United, and Alaska. Use the sign test with a 0.05
Refer to the same data from Exercise 2. Use a 0.05 significance level with the Wilcoxon signed-ranks test to test the claim that differences between fares for flights scheduled 1 day in advance and
Refer to the following ages at inauguration of the elected presidents of the United States (from Data Set 12 in Appendix B). Test for randomness above and below the mean. Do the results suggest an
Each year, U.S. News and World Report publishes rankings of colleges based on statistics such as admis¬sion rates, graduation rates, class size, faculty-student ratio, faculty salaries, and peer
The author conducted a study of the accuracy of weather forecasts by recording the actual high temperatures along with the high temperatures that were forecast 5 days earlier. Differences (actual
The author conducted a study of the accuracy of weather forecasts by recording the actual high temperatures along with the high temperatures that were forecast 5 days earlier. Differences (actual
Listed below are skull breadths obtained from skulls of Egyptian males from three different epochs. Use a 0.05 significance level to test the claim that the samples are from populations with the same
Refer to the preceding exercise and use only the skull breadths from 4000 B.c. and 150 A.D. Use the Wilcoxon rank-sum test with a 0.05 significance level to test the claim that the two samples are
The table below lists weights (lb) of plastic and food disposed in one week (from Data Set 23 in Appendix B). Use rank correlation with a 0.05 significance level to test for a correlation between
The values are the numbers of credit hours taken in the current semester by full-time students of the author.a. Which of the following best describes the sample: simple random sample, voluntary
Use the given data to test the claim that the sample is from a population with a mean greater than 14 hours. The values are the numbers of credit hours taken in the current semester by full-time
Use the given data to test the claim that the sample is from a population with a median greater than 14 hours. Use the sign test with a 0.05 significance level.The values are the numbers of credit
Use the data to construct a 95% confidence interval estimate of the number of credit hours taken by the population of full-time students. Write a brief statement that interprets the result.The values
Listed below are prices (dollars), quality scores, and ranks (1 = best) for six different 3D televisions. Use a 0.05 significance level to test for a linear correlation between price and quality
Refer to the prices and ranks from the preceding exercise. Use a 0.05 significance level to test for a correlation between price and rank.
In a study of 740 pay telephones in New York City underground subway stations, it was found the 229 were not functioning. Construct a 95% confidence interval estimate of the proportion of all such
Advances in technology are dramatically affecting different aspects of our lives. For example, the number of daily newspapers is decreasing because of easy access to Internet and television news. To
Repeat Exercise 5 assuming that the size of each batch is 100 instead of 10,000. Compare the control chart to the one found for Exercise 5. Comment on the general quality of the manufacturing process
In each of recent and consecutive years, 100,000 people in the United States were randomly selected and the number who were victims of violent crime was determined, with the results listed below.
In each of recent and consecutive years of presidential elections, 1000 people of voting age in the United States were randomly selected and the number who voted was determined, with the results
In each of several consecutive days of production of cola cans, 500 cans are tested and the numbers of defects each day are listed below. What action should be taken?
The SmartBatt company manufactures batteries for smart phones. Listed below are numbers of defects in batches of 200 randomly selected in each of 15 consecutive days of production. What action should
After finding the values of the mean and range for each year, find the values of x, and R. Then find the values of LCL and UCL for an R chart and find the values of LCL and UCL for an x chart.Refer
Let each subgroup consist of the 6 values within a year. Construct an R chart and determine whether the process variation is within statistical control. If it is not, identify which of the three
Let each subgroup consist of the 6 values within a year. Construct an x chart and determine whether the process mean is within statistical control. If it is not, identify which of the three
Construct a run chart for the 48 values. Does there appear to be a pattern suggesting that the process is not within statistical control?Refer to the amounts of energy consumed in the
In a survey conducted by Opinion Research Corporation, randomly selected adults were asked what is inappropriate in the workplace. Among 1000 responses, 55% said that it is inappropriate to wear
Based on the results in Exercise 1, assume that there is a 0.55 probability of randomly selecting an adult and getting someone who believes that it is inappropriate to wear shorts at work. a. What is
In 1908, William Gosset published the article €œThe Probable Error of a Mean€ under the pseudonym of €œStudent€ (Biometrika, Vol. 6, No. 1). He included the data listed below for yields
Test Refer to the same sample data given in the preceding exercise. Assume that the experiment was conducted to determine whether the new method of using kiln-dried seed is better. Conduct an
Using the data given in Exercise 3, find the mean and standard deviation of each of the two samples, then informally compare the results.
Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 15.2 cm and a standard deviation of 2.5 cm
What is the difference between a voluntary response sample and a simple random sample? Which is generally better for the use of statistical methods?
Table 14-1 lists process data consisting of the weights (g) of quarters, and the United States Mint uses a manufacturing process designed to result in a mean weight equal to 5.670 g. If recent x and
Consider process data consisting of the amounts of Coke (in oz) in randomly selected cans of regular Coke. The process is to be monitored with x and R control charts based on samples of 50 cans
When using control charts to monitor a process, why is it necessary to include an x chart and an R chart? Why can’t we use just one of those control charts?
Shown below are an x chart (top) and an R chart (bottom) obtained by using the monthly elevations of Lake Mead at Hoover Dam (based on data from the U.S. Department of the Interior). The elevations
After finding the sample mean and sample range for each of the 25 days, find the values of x and R. Also find the values of LCL and UCL for an R chart, then find the values of LCL and UCL for an x
Find the values of x and R. Also find the values of LCL and UCL for an R chart, then find the values of LCL and UCL for an x chart.Refer to the following annual temperatures (°C) of the earth for
Treat the 10 measurements from each decade as a sample and construct an x chart. What does the result suggest?Refer to the following annual temperatures (°C) of the earth for each of the past 50
Treat the the 50 consecutive measurements from the 50 years as individual values and construct a run chart. What does the result suggest?
In this section we described control charts for R and x based on ranges. Control charts for monitoring variation and center (mean) can also be based on standard deviations. An s chart for monitoring
An x chart based on standard deviations (instead of ranges) is made by plotting sample means with a centerline at x and control limits at x + A3s and x A3s, where A3 is found in Table 14-2 and s is
A half dollar is considered to be defective if it deviates substantially from these specifications: The weight is 11.340 g, the diameter is 30.61 mm, the thickness is 2.15 mm, the composition is
After constructing a control chart for the proportions of defective dimes, it is concluded that the process is within statistical control. Does that imply that almost all of the dimes meet the
Listed below are the numbers of defective dimes in successive batches of 10,000 randomly selected on consecutive days of production? 32 21 25 19 35 34 27 30 26 33
The World Bank provides economic data on most of the world’s countries at their website (databank.worldbank.org/data/home.aspx). Select 5 indicators that they provide and answer the questions above
A listing posted by the Arby’s restaurant chain gives, for each of the sandwiches it sells, the type of meat in the sandwich, number of calories, and serving size in ounces. The data might be used
A school in the northeastern United States is concerned with the recent drop in female students in its MBA program. It decides to collect data from the admissions office on each applicant, including:
An internationally recognized MBA program outside of Paris intends to also track the GPA of the MBA students and compares MBA performance to standardized test scores over a six-year period
A start-up company is building a database of customers and sales information. For each customer, it records name, ID number, region of the country (1 = East, 2 = South, 3 = Midwest, 4 = West), date
Business analysts hoping to provide information helpful to grape growers sent out a questionnaire to a sample of growers requesting these data about vine-yards: size, number of years in existence,
The Spectrem provides services for the affluent and retirement markets. In a recent survey, they found that millionaires tend to prefer dogs to cats from a question asking them to list the pets they
The Environmental Protection Agency (EPA) tracks fuel economy of automobiles. Among the data EPA analysts collect from the manufacturer are the manufacturer (Ford, Toyota, etc.), vehicle type (car,
In 2013, Consumer Reports published an article comparing smart phones. It listed 46 phones, giving brand, price, display size, operating system (Android, iOS, or Windows Phone), camera image size
Zagat.com provides ratings from customer experiences on restaurants. For each restaurant, the percentage of customers that liked it, the average cost and ratings of the food, decor, and service (all
L.L. Bean is a large U.S. retailer that depends heavily on its catalog sales. It collects data internally and tracks the number of catalogs mailed out, the number of square inches in each catalog,
An online survey of students in a large MBA Statistics class at a business school in the northeastern United States asked them to report their total personal investment in the stock market ($), total
A study on the potential for developing theme parks in various locations throughout Europe in 2013 collects the following information: the country where the proposed site is located, estimated cost
The 2.5-mile Indianapolis Motor Speedway has been the home to a race on Memorial Day nearly every year since 1911. Even during the first race there were controversies. Ralph Mulford was given the
The Kentucky Derby is a horse race that has been run every year since 1875 at Churchill Downs, Louisville, Kentucky. The race started as a 1.5-mile race, but in 1896 it was shortened to 1.25 miles
Referring to the real estate data table of Exercise 1,a) For each variable, would you describe it as primarily categorical, or quantitative? If quantitative, what are the units? If categorical, is it
Number of motorcycles sold by a dealership in each month of 2014.
Average diameter of trees brought to a saw mill in each week of a year.
Referring to the bookstore data table of Exercise 2,a) For each variable, would you describe it as primarily categorical, or quantitative? If quantitative, what are the units? If categorical, is it

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