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elementary statistics

Questions and Answers of Elementary Statistics

Forecasting hurricanes has become a fine art in Florida. It takes a combination of meteorology and statistics to build forecast models. The following probability distribution was reported in “What
A USA Snapshot (March 10, 2005) presented a bar graph depicting business travelers’ impression of wait times in airport security lines over the past 12 months. Statistics were derived from a Travel
Test the following function to determine whether it is a probability function. If it is not, try to make it into a probability function.a. List the distribution of probabilities and sketch a
Probabilities for events A, B, and C are distributed as shown in the figure. Find:a. P(A and B)b. P(A or C)c. P(A C) A 0.2 20 C 0.1 0.1 0.1/ 0.1 0.2 0.1 0.1 B
This bar graph shows the number of registered automobiles in each of several countries.a. Name at least two countries not included in the information.b. Why are all probabilities resulting from these
Assuming that a woman is equally likely to bear a boy as a girl, use a tree diagram to compute the probability that a four-child family consists of one boy and three girls.4.139 Skillbuilder Applet
P(G) 0.5, P(H) 0.4, and P(G and H) 0.1(see the diagram).a. Find P(G H).b. Find P(H G).c. Find P(H).d. Find P(G or H).e. Find P(G or H).f. Are events G and H mutually exclusive? Explain.g. Are
Skillbuilder Applet Exercise demonstrates the law of large numbers and also allows you to see if you have psychic powers. Repeat the simulations at least 50 times, guessing between picking either a
Use a random-number table or a computer to simulate rolling a pair of dice 100 times.a. List the results of each roll as an ordered pair and the sum.b. Prepare an ungrouped frequency distribution and
The Weather Underground, Inc., provides a trip planner on the Internet. The weather statistics they post are based on searched dates from 1975 to present. You are planning a trip from March 1 to
The U.S. Department of Transportation annually reports the number of consumer complaints against the top U.S. airlines by category. Following are the figures for 2002.If one of these complaints is
Refer to the scatter diagram that follows.b. Find the sample size.c. What is the smallest value reported for the output variable?d. What is the largest value reported for the input variable?e. Does
This equation gives a relationship that exists between b1 and r:b. Verify this equation using formulas (3.2) and(3.6). SS(x) r = b SS (y) X 4 a. Verify the equation for these data: 3 2 3 0 y 11 8 6 7
The accompanying “Emergency cash stash”graphic lists in percentages the distributions for the amount both genders have saved for emergencies.a. Identify the population, the variables, and the
The following graph shows the relationship between three variables: number of licensed drivers, number of registered vehicles, and the size of the resident population for the United States from 1961
Skillbuilder Applet Exercise provide practice in constructing scatter diagrams to match given correlation coefficients.a. After placing just 2 points, what is the calculated r value for each scatter
Skillbuilder Applet Exercise matches correlation coefficients with their scatter diagrams.After several practice rounds using “New Plots,” explain your method of matching. Plot D Pot r=0.56 A
Manatees swim near the surface of the water.They often run into trouble with the many powerboats in Florida. Consider the graph that follows.a. What two groups of subjects are being compared?b. What
Estimate the correlation coefficient for each of the following:
[EX03-034] The following table lists the percents of students who receive free or reduced-price lunches compared with the percents who passed the reading portion of the state exam. The results are
Growth charts are commonly used by a child’s pediatrician to monitor a child’s growth.Consider the growth chart that follows.a. What are the two variables shown in the graph?b. What information
“The perfect age” graphic shows the results from a 9 2 contingency table for one qualitative and one quantitative variable.a. Identify the population and name the qualitative and quantitative
The “Outlook for business travelers” graphic shows two circle graphs, each with four sections.This same information could be represented in the form of a 2 4 contingency table of two qualitative
The results of a consumer study completed at Corner Convenience Store are reported in the accompanying histogram. Answer each question.a. What is the class width?b. What is the class midpoint for the
The following dotplot shows the number of attempted passes thrown by the quarterbacks for 22 of the NFL teams that played on one particular Sunday afternoon.a. Describe the distribution, including
One of the ways that students pay for college is to borrow money. These loans eventually must be paid back, and the accompanying divided bar graph shows the monthly debt that many face after
There are many types of statistical graphs one can choose from when picturing a set of data.The “divided bar graph” shown here is an alternative to the circle graph.a. Construct a circle graph
The supplies needed for a baby during his or her first year can be expensive—averaging $5000, as shown in this divided bar graph.a. Construct a circle graph showing this same information.b.
“Who believes in the 5-second rule?” Most people say food dropped on the floor is not safe to eat.a. Draw a circle graph depicting the percentages of adults for each response.b. If 300 adults are
[EX02-170] A Champions Tour professional golfer is not expected to play in all the available tournaments in the course of a season. The number of tournaments played by each of the 2004 tour’s top
[EX02-168] The USA Snapshot “Paydown after graduation” reports that undergraduates who take loans average $16,500 of debt at graduation.By percentage, the amount of their monthly debt is shown
Pediatric dentists say a child’s first dental exam should occur between ages 6 months and 1 year. The ages at first dental exam for a sample of children are shown in the distribution:a. Find the
A survey asked respondents to list the“number of telephones” per household, x; results are shown here as a frequency distribution.d. Explain why (i) the “sum of the x-column” has no
The graphic “Valentine’s Day spending plan”shows a relative frequency distribution. This graph qualifies as a “tricky graph.”a. Is the graph a bar graph or a histogram? Explain.b. How does
Skillbuilder Applet Exercise matches means and standard deviations with corresponding histograms.After several practice rounds using “Start Over,” explain your method of matching. Plot A Answers
Skillbuilder Applet Exercise matches means with corresponding histograms.After several practice rounds using“New Plots,” explain your method of matching. Plot A Answers Start Over 130 140 150 160
2.64 Skillbuilder Applet Exercise demonstrates the effect one data value can have on the mean and on the median.a. Move the red dot to the far right. What happens to the mean? What happens to the
2.59 Skillbuilder Applet Exercise demonstrates the balancing effect of the mean. A plot is given with one data point at 10.Add more blocks by pointing and clicking on the desired location on the plot
2.56 The levels of various compounds resulted in the distribution graphs that follow. They all seem to be quite symmetrical about their centers, but they differ in their spreads.a. For which
2.54 Undergraduates who use loans to pay for college average $16,500 in debt when they graduate.The relative frequency distribution of their monthly debt after graduation is shown here:Source: USA
2.50 Skillbuilder Applet Exercise demonstrates the effect that the number of classes or bins has on the shape of a histogram.a. What shape distribution does using one class or bin produce?b. What
2.40 Skillbuilder Applet Exercise demonstrates the procedure of transforming a stem-and-leaf display into a histogram.Type the leaves for the number of stories into the stem-and-leaf display. Click
2.39 [EX02-039] A survey of 100 resort club managers on their annual salaries resulted in the following frequency distribution:a. The data value “35” belongs to which class?b. Explain the meaning
2.38 Figuring where lightning strikes will occur is a near impossible task. When lightning strikes occur, however, has become more predictable based on research. For a small area in Colorado, data
2.25 [EX02-025] The amounts shown here are the fees charged by Quik Delivery for the 40 small packages it delivered last Thursday afternoon:a. Construct a stem-and-leaf display.b. Based on the
2.24 [EX02-024] Forbes.com posted the 5-year(2000 to 2004) total returns, in percents, for 17 banking industry companies.a. Construct a stem-and-leaf display of the data.b. Based on the stem-and-leaf
2.22 A computer was used to construct the dotplot at the bottom of the page.a. How many data values are shown?b. List the values of the five smallest data.c. What is the value of the largest data
2.20 [EX02-020] As baseball players, Babe Ruth and Hank Aaron were well known for their ability to hit home runs. Mark McGwire and Sammy Sosa became well known for their ability to hit home runs
2.16 [EX02-016] The world’s cocoa production in 2004–2005 is predicted to decline following a record 3396 MT crop in 2003–2004. Most of the reduction is expected to occur in West Africa, with
2.15 The final-inspection defect report for assembly line A12 is reported in a Pareto diagram.a. What is the total defect count in the report?b. Verify the 30.0% listed for “Scratch.”c. Explain
2.11 A shirt inspector at a clothing factory categorized the last 500 defects as follows: 67—missing button, 153—bad seam, 258—improperly sized, 22—fabric flaw. Construct a Pareto diagram for
1.12 The mean checkout time for all customers at Corner Convenience Store is to be estimated by using the mean checkout time for 75 randomly selected customers. Match the items in column 2 with the
1.82 “Drugs of choice,” a chart in a March 2005 Democrat & Chronicle article titled “Pill unhooks heroin’s claws, but few get it,” presents the numbers of people abusing various drugs.
1.76 The 700 Club: Barry Bonds of the San Francisco Giants is on pace to become baseball’s homerun king this season or next. Last year, he joined Hank Aaron and Babe Ruth as the only majorleague
1.75 The following graph shows the relationship between three variables: number of licensed drivers, number of registered vehicles, and the size of the resident population for the United States from
1.71 Harris Interactive conducted an online poll of U.S. adults during December 2004 for the Wall Street Journal Online’s Health Industry Edition.a. What is the population?b. Name at least four
1.40 Skillbuilder Applet Exercise simulates sampling from a population of college students.a. Take 10 samples of size 4 and keep track of the sample averages of hours per week that students study.
1.30 Skillbuilder Applet Exercise simulates taking a sample of size 10 from a population of 100 college students. Take a sample of size 10.a. What is the population?b. Is the population finite or
1.20 Skillbuilder Applet Exercise simulates taking a sample of size 10 from a population of 100 college students. Take one sample and note the outcome.a. Name the attribute variable involved in this
1.11a. What is the population?b. Describe the sample used for this report.c. Identify the variables used to collect this information.d. What is the majority of people going to do with their tax
1.10 Refer to the graphic “Driver cell phone distractions.”a. What group of people was polled?b. How many people were polled?c. What information was obtained from each person?d. Explain the
1.9 International Communications Research (ICR)conducted the 2004 National Spring Cleaning Survey for The Soap and Detergent Association. ICR questioned 1000 American male and female heads of
1.8 Refer to the graphic “America’s students by grade level.”The latest Census report on schools found about 70 million students (27.8% of the population)from nursery school through college.a.
ESP A student majoring in psychology designs an experiment to test for extrasensory perception (ESP). In this experiment, a card is randomly selected from a shuffled deck, and the blindfolded subject
SAT Math Scores of Women The math SAT scores for women are normally distributed with a mean of 496 and a standard deviation of 108.a. If a woman who takes the math portion of the SAT is randomly
Monitoring Dioxin Listed below are measured amounts of dioxin in the air at the site of the World Trade Center on the days immediately following the terrorist attacks of September 11, 2001. Dioxin
Weights of Sugar Packets Refer to Data Set 28 in Appendix B and test the claim that the weights of the sugar packets have a mean equal to 3.5 g, as indicated on the label.If the mean does not appear
Is the New Machine Better? The Medassist Pharmaceutical Company uses a machine to pour cold medicine into bottles in such a way that the standard deviation of the weights is 0.15 oz. A new machine is
Percentage Believing That Elvis Is Alive USA Today ran a report about a University of North Carolina poll of 1248 adults from the southern United States. It was reported that 8% of those surveyed
Are Consumers Being Cheated? The Orange County Bureau of Weights and Measures received complaints that the Windsor Bottling Company was cheating consumers by putting less than 12 oz of root beer in
Voting for the Winning Candidate In a recent presidential election, 611 voters were surveyed, and 308 of them said that they voted for the candidate who won (based on data from the ICR Survey
Percentage of Theme Park Visits Each year, billions of dollars are spent at theme parks owned by Disney, Universal Studios, Sea World, Busch Gardens, and others. A survey of 1233 people who took
Weights of Blue M&Ms Using the weights of only the blue M&Ms listed in Data Set 19 in Appendix B, test the claim that the mean is at least 0.9085 g, the mean value necessary for the 1498 M&Ms to
Weights of Quarters If we refer to the weights (in grams) of quarters listed in Data Set 29 in Appendix B, we find 50 weights with a mean of 5.622 g and a standard deviation of 0.068 g. The U.S.
Interviewing Mistakes An Accountemps survey of 150 executives showed that 44%of them say that “little or no knowledge of the company” is the most common mistake made by candidates during job
Random Generation of Data The TI-83 Plus calculator can be used to generate random data from a normally distributed population. The command randNorm(100,15,50) generates 50 values from a normally
Identifying Hypotheses and Distributions Based on the given conditions, identify the alternative hypothesis and the sampling distribution (normal, t, chi-square) of the test statistic.a. Claim: The
Probability of a Type II Error Refer to Exercise 9. Assuming that s is actually 4.0, findb, which denotes the probability of a type II error. See Exercise 19 in Section 7-4, and modify the procedure
Last-Digit Analysis The last digits of sample data are sometimes used in an attempt to determine whether the data have been measured or simply reported by the subject.Reported data often have last
Effect of Outlier When using the hypothesis testing procedure of this section, will the result be dramatically affected by the presence of an outlier? Describe how you arrived at your response.
Finding Critical Values of x2 Repeat Exercise 18 using this approximation (with k and z as described in Exercise 18):
Finding Critical Values of x2 For large numbers of degrees of freedom, we can approximate critical values of x2 as follows:Here k is the number of degrees of freedom and z is the critical value,
Heights of Women Anthropometric survey data are used to publish values that can be used in designing products that are suitable for use by adults. According to Gordon, Churchill, et al., women have
Weights of Men Anthropometric survey data are used to publish values that can be used in designing products that are suitable for use by adults. According to Gordon, Churchill, et al., men have
Systolic Blood Pressure for Women Systolic blood pressure results from contraction of the heart. Based on past results from the National Health Survey, it is claimed that women have systolic blood
Volumes of Pepsi A new production manager claims that the volumes of cans of regular Pepsi have a standard deviation less than 0.10 oz. Use a 0.05 significance level to test that claim with the
Supermodel Heights Use a 0.05 significance level to test the claim that heights of female supermodels vary less than the heights of women in general. The standard deviation of heights of the
Supermodel Weights Use a 0.01 significance level to test the claim that weights of female supermodels vary less than the weights of women in general. The standard deviation of weights of the
Body Temperatures In Section 7-4, we tested the claim that the mean body temperature is equal to 98.6°F, and we used sample data given in Data Set 4 in Appendix B.The body temperatures taken at
Bank Customer Waiting Times With individual lines at its various windows, the Jefferson Valley Bank found that the standard deviation for normally distributed waiting times on Friday afternoons was
Statistics Test Scores Tests in the author’s past statistics classes have scores with a standard deviation equal to 14.1. One of his recent classes has 27 test scores with a standard deviation of
Manufacturing Aircraft Altimeters The Stewart Aviation Products Company uses a new production method to manufacture aircraft altimeters. A simple random sample of 81 altimeters is tested in a
Variation in Pistons When designing a piston to be used for a pump for transferring liquid solutions, engineers specified a mean of 0.1 in. as the target for the piston radius. The maximum standard
Variation in Peanut M&Ms Use a 0.01 significance level to test the claim that peanut M&M candies have weights that vary more than the weights of plain M&M candies.The standard deviation for the
Probability of Type II Error Refer to Exercise 28 and assume that you’re testing the claim that m . 40 mg. Findb, the probability of a type II error, given that the actual value of the population
Finding Critical t Values When finding critical values, we sometimes need significance levels other than those available in Table A-3. Some computer programs approximate critical t values by
Effect of an Outlier Repeat Exercise 25 after changing the first value from 5.40 to 540. Based on the results, describe the effect of an outlier on a t test.
Using the Wrong Distribution When testing a claim about a population mean with a simple random sample selected from a normally distributed population with unknown s, the Student t distribution should
Using Computer Results Refer to the Minitab display in Exercise 22.If the claim is changed from “greater than 420 h” to “not equal to 420 h,” how are the test statistic, P-value, and
Sodium in Cereal Refer to Data Set 16 in Appendix B and test a nutritionist’s claim that “the average box of cereal contains more than 6 mg of sodium per gram of cereal.” If 6 mg of sodium per

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