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Elementary Statistics 11th Edition Robert R. Johnson, Patricia J. Kuby - Solutions

Blogging is a hot topic nowadays. A €œblog€ is an Internet log. Blogs are created for personal or professional use. According to the Xtreme Recruiting website (www.xtremerecruiting.org/), there is a new blog born every 7 seconds€”and quite a few people are reading
The November 12, 2009, USA Today Snapshot €œRabies in cats on the rise€ reported that almost 7000 animals were reported to have rabies in 2008. Utilizing information from the Journal of the American Veterinary Medical Association, the following rabies cases were logged for cats
The athletic director at a large high school wants to compare the proportions of different kinds of ankle injuries that occur to his school€™s basketball players and volleyball players. Inspection of last year€™s records revealed the following number of ankle injuries for each
Using the notation seen in Exercise 11.4, name and find the critical values of x2.
Students use many kinds of criteria when selecting courses. €œTeacher who is a very easy grader€ is often one criterion. Three teachers are scheduled to teach statistics next semester. A sample of previous grade distributions for these three teachers is shown here.At the 0.01
Fear of darkness is a common emotion. The following data were obtained by asking 200 individuals in each age group whether they had serious fears of darkness. At a = 0.01 do we have sufficient evidence to reject the hypothesis that €œThe same proportion of each age group has serious fears
According to a report from the Substance Abuse and Mental Health Services Administration, food-service workers have the highest rate for smoking cigarettes: 45% of food-service workers reported smoking cigarettes in the past month. Do some careers lend themselves to cigarette smoking more than
All new drugs must go through a drug study before being approved by the U.S. Food and Drug Administration (FDA). A drug study typically includes clinical trials whereby participants are randomized to receive different dosages as well as a placebo but are unaware of which group they are in. To
Are younger and younger people able to obtain illegal guns? According to the October 11, 2009, Rochester, NY, Democrat & Chronicle article €œThe Gun Used to Shoot DiPonzio,€ which cited a 14-year-old shooting a police officer, it appears that the number of people in younger age
Applied Example 11. 7 reports percentages describing people’s preferences with regard to how potatoes are prepared. Do you believe there is a significant difference between the four regions of America with regard to the percentage who prefer baked? Notice that the article does not mention the
The psychology department at a certain college claims that the grades in its introductory course are distributed as follows: 10% A’s, 20% B’s, 40% C’s, 20% D’s, and 10% F’s. In a poll of 200 randomly selected students who had completed this course, it was found that 16 had received A’s;
When interbreeding two strains of roses, we expect the hybrid to appear in three genetic classes in the ratio 1_3_4. If the results of an experiment yield 80 hybrids of the first type, 340 of the second type, and 380 of the third type, do we have sufficient evidence to reject the hypothesized
A sample of 200 individuals are tested for their blood type, and the results are used to test the hypothesized distribution of blood types:At the 0.05 level of significance, is there sufficient evidence to show that the stated distribution is incorrect?
As reported in USA Today, about 8.9 million families sent students to college this year and more than half live away from home. Where students live: Parents’ or guardian’s home...... 46% Campus housing................. 26% Off-campus rental................... 18% Own off-campus
Using the notation seen in Exercise 11.4, name and find the critical allures of x2
Over the years, African-American actors in major cinema releases have been more likely than white actors to have major roles in comedies. The table shows the percent of all roles by type of picture.The next table shows a sample of the latest released films with the number of leading roles played by
Most golfers are probably happy to play 18 holes of golf whenever they get a chance to play. Ben Winter, a club professional, played 306 holes in 1 day at a charity golf marathon in Stevens, Pennsylvania. A nationwide survey conducted by Golf magazine over the Internet revealed the following
The U.S. census found that babies enter the world during the various months in the proportions that follow.A random sample selected from the birth records for a large metropolitan area resulted in the following data: a. Do these data provide sufficient evidence to reject the claim
The weights (x) of 300 adult males were determined and used to test the hypothesis that the weights are normally distributed with a mean of 160 lb and a standard deviation of 15 lb. The data were grouped into the following classes.Using the normal tables, the percentages for the classes are 2.28%,
Do you have a favorite €œcomfort food€? How do you obtain it? The USA Today Snapshot lists three methods used by Americans and the percentage who use each method. Which category do you belong to? A random sample of 120 Americans living on the East Coast was asked,
The following table gives the color counts for a sample of 30 bags (47.9-gram size) of M&€™s.Before the Global Color Vote (GCV) of 2002, the target percentage for each color in the six-color mix was as follows: brown, 30%; red and yellow, 20%; blue, green, and orange, 10%. a. Does case 1
Adults 21 and older volunteer from one to nine hours each week at a center for disabled senior citizens. The program recruits adult community college students, four-year college students, and nonstudents. The table below lists a sample of the volunteers, their number of hours per week, and the
A manufacturer of women€™s shoes wishes to compare the distribution of defects found in the shoes produced by the three shifts of workers in his plant. A sample of shoes with defects is classified as to type of defect and production shift.a. Would the proportions of the four defects being
The following table shows the number of reported crimes committed last year in the inner part of a large city. The crimes were classified according to the type of crime and the district of the inner city where it occurred. Do these data show sufficient evidence to reject the hypothesis that the
Based on the results of a survey questionnaire, 400 individuals were classified as politically conservative, moderate, or liberal. In addition, each person was classified by age, as shown in the following table.Is there sufficient evidence to reject the hypothesis that €œPolitical
Verify that Applied Example 11. 3, “Birth Days” (p. 554), is a multinomial experiment. Be specific. a. What is one trial? b. What is the variable? c. What are the possible levels of results from each trial?
On May 21, 2004, the National Center for Chronic Disease Prevention and Health Promotion, the Centers for Disease Control and Prevention, reported the results of the Youth Risk Behavior Surveillance€” United States, 2003.The report split the sample of 15,184 American teenagers into grade
Based on data from the U.S. Census Bureau, the National Association of Home Builders forecasted a rise in homeownership rates for this past decade. Part of the forecast predicted new housing starts by region. The following table shows what they forecastedDo the data present sufficient evidence to
Four brands of popcorn were tested for popping. One hundred kernels of each brand were popped, and the number of kernels not popped was recorded in each test (see the following table). Can we reject the null hypothesis that all four brands pop equally? Test ata. Solve using the p-value approach. b.
An average of two players per boys€™ or girls€™ high school basketball team are injured during a season. The following table shows the distribution of injuries for a random sample of 1000 girls and 1000 boys taken from the season records of all reported injuries.Does this sample
€œHave you designated on your driver€™s license that you are an organ donor?€We have all heard this question, and the word must be getting out, according to the March 30, 2005, article €œOrgan Transplants Reach New High of Almost 27,000 in 2004.€
Last year€™s work record for absenteeism in each of four categories for 100 randomly selected employees is compiled in the following table. Do these data provide sufficient evidence to reject the hypothesis that the rate of absenteeism is the same for all categories of employees? Use a =
If you were to roll a die 600 times, how different from 100 could the observed frequencies for each face be before the results would become significantly different from equally likely at the 0.05 level?
Consider the following set of data.a. Compute the value of the test statistic z_ that would be used to test the null hypothesis that p1 = p2 where p1 and p2 are the proportions of €œyes€ responses in the respective groups. b. Compute the value of the test statistic x2 that
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements: a. The five numbers 1, 2, 3, 4, and 5 are equally likely to be drawn. b. The multiple-choice question has a history of students selecting answers in the ratio of 2:3:2:1. c. The
An analysis of variance experiment with level A containing 10 data values; level B, 12. data values; level C, 10 values; level D,12. values; level E, 9 values; and level F, 10 values was analyzed using MINITAB.a. Verify the three values for df shown on the printout. Also verify the relationship
Do the data shown in the boxplot have a greater amount of variability within levels A, B, C, and D or between the four levels? Explain.
Referring to Applied Example 12. .4 on page 588: a. Does the category, city, appear to have an effect on the average daily parking rate? Explain. b. Explain how cities could be used as categories to organize data for one-way ANOVA. What would be used as the levels? What would be used as the data
The amount of monthly rainfall varies from month to month and from city to city. Applied Example12. .5 on page 589 suggests that the average monthly rainfall is affected by both the month and the location. a. What variable was used to collect the data used to find the monthly averages shown in
Consider the following table for a single-factor ANOVA. Find the following:a. x1, 2b. x2, 1c. C1d. ˆ‘xe. ˆ‘(Ci)2
The following table of data is to be used for singlefactor ANOVA. Find each of the following:a. x3, 2b. x4, 3c. C3d. ˆ‘xe. ˆ‘(Ci)2
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements: a. The mean value of x is the same at all five levels of the experiment. b. The scores are the same at all four locations c. The four levels of the test factor do not
Find the p-value for each of the following situations:
For the following ANOVA experiments, determine the critical region(s) and critical value(s) that are used in the classical approach for testing the null hypothesis.
To compare commuting times in various locations, independent random samples were obtained from the six cities presented in €œThe Morning Rush.€The samples were from workers who commute to work during the 8:00 a.m. rush hour.a. Construct a graphic representation of the data
Suppose that an F-test (as described in this chapter using the p-value approach) has a p value of 0.04. a. What is the interpretation of p-value = 0.04 ? b. What is the interpretation of the situation if you had previously decided on a 0.05 level of significance? c. What is the interpretation of
Suppose that an F-test (as described in this chapter using the classical approach) has a critical value of 2.2, as shown in this figure:a. What is the interpretation of a calculated value of F larger than 2.2? b. What is the interpretation of a calculated value of F smaller than 2.2? c. What is the
a. State the null hypothesis, in a general form, for the one-way ANOVA. b. State the alternative hypothesis, in a general form, for the one-way ANOVA. c. What must happen in order to “reject Ho”? Answer for both the p-value approach and the classical approach. d. How would a decision of
The following two excerpts were taken from “Documentation of Structured Analysis for Reviewing Scientifically-Based Research: Instructional Strategies and Programs,” reviewed for NCTM on August 28, 2004. I. A statistically significant main effect was obtained for group only, F (1, 31) = 6.23 p
An article reported on a study that examined the cultural literacy of developmental, nondevelopmental, and English as a Second Language (ESL) college freshmen.a. How many student scores were in the samples? b. The students were divided into how many groups? c. Given the SS and df values, verify the
Two new drugs are being tested for their effect on the number of days a patient must remain hospitalized after surgery. A control group is receiving a placebo, and two treatment groups are each receiving one of two new drugs, both developed to promote recovery. The null hypothesis is that there is
An employment agency wants to see which of three types of ads in the help-wanted section of local newspapers is the most effective. Three types of ads (big headline, straightforward, and bold print) were randomly alternated over a period of weeks, and the number of people responding to the ads was
A new operator was recently assigned to a crew of workers who perform a certain job. From the records of the number of units of work completed by each worker each day last month, a sample of size 5 was randomly selected for each of the two experienced workers and the new worker. At the 0.05 level
Random samples of 2009 pickup trucks with 4-cylinder, 6-cylinder, and 8-cylinder engines were obtained. Each pickup truck was tested for miles per gallon in city driving.Is there significant evidence to reject the hypothesis that the mpg for pickup trucks is the same for all three engine sizes? Use
Random samples of 2009 pickup trucks with 4-cylinder, 5-cylinder, 6-cylinder, and 8-cylinder engines were obtained. Each pickup truck was tested for miles per gallons in highway driving. Is there significant evidence to show that the mpg for pickup trucks is not the same for all four engine sizes?
A number of sports enthusiasts have argued that Major League Baseball players on teams in the Central Division have an unfair advantage over coastal players in the Western and Eastern Divisions. This is because the impact due to the differences in time is likely to be greater when playing on the
Cities across the United States have restaurants that offer themes associated with foreign countries. German-style food and drink have become popular since many communities started hosting Oktoberfests, but authentic German food restaurants offer the fare all year long. The following ratings, based
Does highest attained level of education influence the number of hours of TV that people watch per day? Random samples were identified from each level of education, and the hours of television watched per day by each person surveyed.a. Do the sample data show significant evidence to conclude that
A study was conducted to assess the effectiveness of treating vertigo (motion sickness) with a transdermal therapeutic system (TTS; a patch worn on the skin).Two other treatments, both oral (one pill containing a drug and one a placebo), were used. The age and the gender of the patients for each
The NBA is a big man€™s game. Average height for the league is about 6 feet 7 inches, as reported on the NBA website for the 2007€“2008 season. Generally, guards average 6 ft 4 in., forwards average 6 ft 9 in., and centers average 7 feet. A random sample of 2008 NBA players was
To compare the commuting times in various locations, independent and random samples were obtained in each of six different U.S. cities, as displayed in Section 12. .1’s The Morning Rush. Using the commute time data located in Exercise 12. .2 on page 586: a. Construct a box plot showing the six
Thirty-nine counties from the sixstate upper Midwest area of the United States were randomly selected from the USDA-NASS website and the following data on oat-production yield per acre were obtained.a. Do these data show a significant difference in the mean yield rates for the six states? Use a =
Let x = a person€™s €œideal age€ in years. Independent and random samples were obtained from U.S. adults in each of six different age groups.a. Construct a side-by-side boxplot showing the €œideal age€ for each of the six age groups.What does this
a. Calculate the mean commute time for each city depicted in Exercise 12. .2. b. Does there seem to be a difference among the mean one-way commute times for these six cities? c. Calculate the standard deviation for each city’s commute time. d. Does there seem to be a difference among the standard
Stacey is a student at a community college. She figured, being at a community college, that the majority of students probably work a job in addition to their studies. Keeping to daytime classes, Stacey considered that both gender and type of course may have an effect on the type of student and the
The March 14, 2009, Boston Globe article €œBargains on the Menu€”and a Side of Jitters€ reported concerns that Restaurant Week would not be well attended due to the economy. Local restaurants were coming up with special promotions to draw past and new customers.
A local packaging plant implements various production lines based on the product to be packaged. Each line is for a different product, some being more complicated than others. With several lines running on a daily basis, concern over production rates surfaced due to the variation in the rates.
Albert Michelson, the first American citizen to be awarded a Nobel Prize in Physics, conducted many experiments in determining the velocity of light in air. Following is an excerpt of five trials of 20 measurements each taken by Michelson from June 5 to July 2, 1879. The measurements have had
Mr. B, the manager at a large retail store, is investigating several variables while measuring the level of his business. His store is open every day during the year except for New Year€™s Day, Christmas, and all Sundays. From his records, which cover several years prior, Mr. B has
Mr. B, the manager of the retail store in Exercise 12. .44, has seen that the mean number of customers per day varies by month, and he is now wondering if month has a similar effect on number of items purchased. a. Do you think “month” has an effect on the mean number of items purchased per
Mr. B, the manager of the retail store in Exercise 12. .44, has seen that the mean number of customers per day and the mean number of items purchased (Exercise 12. .45) are affected by the month, and he is now wondering if month has a similar effect on the total cost of items purchased. a. Do you
Samples of peanut butter produced by three different manufacturers were tested for salt content (in milligrams), with the following results:Is there a significant difference in the mean amount of salt in these samples? Use a = 0.05 . a. State the null and alternative hypotheses. b. Determine the
A new all-purpose cleaner is being testmarketed by placing sales displays in three different locations within various supermarkets.The number of bottles sold from each location within each of the supermarkets is reported here:a. State the null and alternative hypotheses for testing that
Does it really matter financially where you grocery shop? Are the prices at one grocery store consistently higher or lower than those at another? €œShopping the grocers,€ an article in the Democrat & Chronicle, featured a comparison of products bought at four local
Referring to the data in 12. .2: a. Construct the 95% confidence interval for the mean commute time for Atlanta and Boston. b. Based on the confidence intervals found in part a, does it appear that the mean commute time is the same or different for these two cities? Explain. c. Construct the 95%
An experiment was designed to compare the lengths of time that four different drugs provide pain relief after surgery.The results (in hours) follow.Is there enough evidence to reject the null hypothesis that there is no significant difference in the lengths of pain relief provided by the four drugs
A certain vending company€™s soft drink dispensing machines are supposed to serve 6 oz of beverage. Various machines were sampled, and the resulting amounts of dispensed drink (in ounces) were recorded, as shown in the following table.Does this sample evidence provide sufficient reason to
To compare the effectiveness of three different methods of teaching reading, 26 children of equal reading aptitude were divided into three groups. Each group was instructed for a given period of time using one of the three methods. After completing the instruction period, all students were tested.
The distance required to stop a vehicle on wet pavement was measured to compare the stopping power of four major brands of tires. A tire of each brand was tested on the same vehicle on a controlled wet pavement. The resulting distances follow.At a = 0.05 is there sufficient evidence to conclude
The following table gives the number of arrests made last year for violations of the narcotic drug laws in 24 communities. The data given are rates of arrest per 10,000 inhabitants.At a = 0.05 , is there sufficient evidence to reject the hypothesis that the mean rates of arrests are the same in all
Seven golf balls from each of six manufacturers were randomly selected and tested for durability. Each ball was hit 300 times or until failure occurred, whichever came first.Do these sample data show sufficient reason to reject the null hypothesis that the six different brands tested withstood the
Suburbs, each with its own attributes, are located around every metropolitan area. There is always the €œrich€ one (the most expensive one), the least expensive one, and so on. The dollar amounts of county transfer taxes paid on homes from five suburbs follow.a. Do the sample
The question arises every year when the playoffs begin in the National Football League: €œWhich division teams are the toughest, East, North, South, or West?€Two ways to measure the strength of the football teams that play are the number of points they score and the number of
Beer is Americans€™ preferred alcoholic beverage. It is estimated that 90 million Americans drink beer and that as much as 20% of all alcohol is consumed by underage persons, with a large portion of that being beer. Many citizens have emphatically promoted increases in alcohol excise
The New York Times December 1, 2009, article €œIn November, Car Sales Show Signs of Stability€ reported that new vehicles were selling at a seasonally adjusted annualized rate of 11 million in November. This rate was much higher than the low rate of 9 million computed earlier
Referring to the data in 12. .2: a. Construct the 95% confidence interval for the mean commute time for Philadelphia and St. Louis. b. Based on the confidence intervals found in part a, does it appear that the mean commute time is the same or different for these two cities? Explain. c. Construct
A study reported in the Journal of Research and Development in Education evaluates the effectiveness of social skills training and cross-age tutoring for improving academic skills and social communication behaviors among boys with learning disabilities. Twenty boys were divided into three groups,
The Bureau of Labor Statistics posts a table of average weekly hours worked by production workers on private, nonfarm payrolls by major industry. These seasonally adjusted data were downloaded from their website January 4, 2010.a. At the 0.05 level of significance, is the evidence sufficient to
Ronald Fisher, an English statistician (1890€“1962), collected measurements for a sample of 150 irises. Of concern were the following variables: species, petal width (PW), petal length, sepal width (SW), and sepal length (all in mm). (Sepals are the outermost leaves that encase the flower
Cicadas are flying, plant-eating insects. One particular species, the 13-year cicada (Magicicada), spends five juvenile stages in underground burrows. During the 13 years underground, the cicadas grow from approximately the size of a small ant to nearly the size of an adult cicada. Every 13 years,
Mr. B, the manager of the retail store in Exercise 12. .44, has seen the effect month has on the mean number of customers per day and is now wondering about the effect day of the week has on the mean number of customers per day. Is the mean number of customers per day affected by the day of the
Mr. B, the manager of the retail store in Exercise 12. .65, has seen the effect day of the week has on the mean number of customers per day and is now wondering if day has a similar effect on number of items purchased. a. Do you think “day of week” has an effect on the mean number of items
Do the similarities seem reasonable? What does this imply about these variables?
For the following data, find SS (error) and show That
For the following data, show that SS(factor) = k1(1 = )2 = k2(2 = )2 = k3(3 = )2 where12, 3 , , are the means for the three factor levels and is the overall mean.
Draw a dotplot of the data in Table 12. .2 (p. 579). Represent the data using the integers 1, 2, and 3, indicating the level of test factor the data are from. Do you see a “difference” among the levels?
An article in the Journal of Pharmaceutical Sciences discusses the change of plasma protein binding of diazepam at various concentrations of imipramine. Suppose the results were reported as follows.The values given represent mean plasma protein binding, and n = 8 for each of the four groups. Find
Refer to the following ANOVA table.a. Find the four missing values. b. Find the calculated value for F, F_.
Consider the “Married Couples’ Heights” scatter diagram presented in “Height Compatibility” on page 612. a. What is the independent variable for this set of data? How does it appear on the scatter diagram? b. What is the dependent variable for this set of data? How does it appear on the
Use a computer to form the extensions table; calculate the summations ˆ‘x, ˆ‘y, ˆ‘x2, ˆ‘xy, ˆ‘y2; and find the SS(x), SS(y), and SS(xy) for the following set of bivariate data.

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