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Elementary Statistics A Step By Step Approach 10th Edition Allan G. Bluman - Solutions
In a correlation test for normality, what correlation is computed?
Regarding normal probability plots,a. What are they?b. What is an important use for them?c. How is one used to assess the normality of a variable?d. Why is the method described in part (c) subjective?
Identify a use of the coefficient of determination as a descriptive measure.
A chi-square independence test is to be conducted to decide whether an association exists between two variables of a population. One variable has six possible values, and the other variable has four. What is the degrees of freedom for the χ2-statistic?
Refer to Exercise 11.43. Assume that the standard deviation of bolt diameters is 0.09 mm.a. Simulate 10,000 bolt diameters.b. Determine the number of bolts whose diameters do not meet the manufacturer’s tolerance specifications.Data from exercise 11.43A hardware manufacturer produces
A hardware manufacturer produces 10-millimeter (mm) bolts. Although the diameters of the bolts can vary somewhat from 10 mm and also from each other, if the variation is too large, too many of the bolts produced will be unusable. The manufacturer must therefore ensure that the standard deviation,
For a χ2-curve with df = 4, determinea. χ20.005.b. χ20.99.
What symbol is used to denote the F-value having area 0.05 to its right? 0.025 to its right? α to its right?
How is an F-distribution and its corresponding F-curve identified?
We considered three hypothesis-testing procedures based on independent simple random samples to compare the means of two populations with unknown standard deviations.a. Identify the three procedures by name.b. List the conditions for using each procedure.c. Identify the test statistic for each
The U.S. median annual income for men in 2014 (in constant dollars) was $35,642. A random sample of recent male college graduates indicated the following incomes. At the 0.05 level of significance, test the claim that the median is more than $35,642. 37,682 36,198 38,850 39,800 31,500 39,750 32,500
Use Table K to determine whether the null hypothesis should be rejected.ws = 22, n = 14, α = 0.10, two-tailed
Listed are the numbers of on-demand movies rented per month for 20 customers of a particular cable service. Test the data for randomness at the 0.05 level of significance. What would have to occur to effect the opposite result? Discuss how the data would have to change. 20 14 14 20 13 6 1 20 17 7
It has been found that many firsttime interviewees commit errors that could very well affect the outcome of the interview. An astounding 77% are guilty of using their cell phones or texting during the interview! A researcher wanted to see if the proportion of male offenders differed from the
State the hypotheses used in the ANOVA test.
What is meant by nonparametric statistics?
Fear of public speaking is a common problem for many individuals. A researcher wishes to see if educating individuals on the aspects of public speaking will help people be more confident when they speak in public. She designs three programs for individuals to complete. Group A studies the aspects
Why is the sign test the simplest nonparametric test to use?
Find the critical value from Table L for the rank correlation coefficient, given sample size n and α. Assume that the test is two-tailed.n = 26, α = 0.05
A manufacturer suggests that the median time a rechargeable battery on an electric grass trimmer will last is 420 minutes. A random sample of 30 newly charged batteries shows that 11 lasted longer than 420 minutes. Is there enough evidence to reject the claim at α = 0.02?
When should nonparametric statistics be used?
What is the difference between the Wilcoxon rank sum test and the Wilcoxon signed-rank test?
Find the critical value from Table L for the rank correlation coefficient, given sample size n and α. Assume that the test is two-tailed.n = 26, α = 0.01
The 2014 women's 1000-meter speed skating winning time was 1:14:02, posted by Zhang Hong of China. In preparation for the 2018 Winter Olympics in Pyeongchang, South Korea several randomly selected students from two different universities posted the following times (rounded to the nearest second).
A psychologist designed a questionnaire to measure the level of depression among her patients. She divided the patients into three groups: never married, married, and divorced. Then she randomly selected subjects from each group and administered a questionnaire to measure their level of depression.
In the sign test, what is used as the test value when n ≤ 25?
Find the sum of the signed ranks. Assume that the samples are dependent. State which sum is used as the test value. 154 152 Pretest 106 85 163 117 106 112 105 Posttest 167 142 143 113 84
Find the critical value from Table L for the rank correlation coefficient, given sample size n and α. Assume that the test is two-tailed.n = 9, α = 0.02
When n > 25, what is used in place of Table J for the sign test?
Find the sum of the signed ranks. Assume that the samples are dependent. State which sum is used as the test value. Pretest 38 62 49 82 25 29 63 74 29 45 51 45 32 74 Posttest 87 71
Find the critical value from Table L for the rank correlation coefficient, given sample size n and α. Assume that the test is two-tailed.n = 13, α = 0.05
What is the parametric equivalent test for the Wilcoxon signed-rank test?
A university dean wishes to see if there is a difference in the number of credits community college students transfer as opposed to students who attend a 4-year college and transfer after 2 years. The data are shown. Use the Wilcoxon rank sum test to test this claim at α = 0.05.
Why does the term distribution-free describe nonparametric procedures?
The sugar content in grams of three different brands of candy bars is shown. At α = 0.05, is there a difference in the number of calories in each type? Brand B 9.2 Brand A 7.6 9.3 Brand C 18.6 16.2 12.3 10.1 10.2 8.4 15.4 11.3 10.2 9.8 18.0 17.3
The median age at first marriage in 2014 for women was 27 years€”the highest it has ever been. A random sample of women€™s ages (in years) from recently applied for marriage licenses resulted in the following set of ages. At α = 0.05, is there sufficient evidence
Use Table K to determine whether the null hypothesis should be rejected.ws = 13, n = 15, α = 0.01, two-tailed
The National Assessment of Educational Progress (U.S. Department of Education) tests mathematics, reading, and science achievement in grades 4 and 8. A random sample of states is selected, and their mathematics achievement scores are noted for fourth- and eighth-graders. At α = 0.05,
Explain what is meant by the efficiency of a nonparametric test.
Use Table K to determine whether the null hypothesis should be rejected.ws = 32, n = 28, α = 0.025, one-tailed
Rank each set of data.25, 68, 36, 63, 36, 74, 39
Use Table K to determine whether the null hypothesis should be rejected.ws = 65, n = 20, α = 0.05, one-tailed
Rank each set of data.88, 465, 587, 182, 243
A random sample of cable from three different manufacturers is tested for breaking strength. The data (in pounds) are shown. At α = 0.05 is there a difference in the breaking strength of the cables? Use the Kruskal-Wallis test. Manufacturer B 416 404 483 Manufacturer A 602 587 433 551
Rank each set of data.18.6, 20.7, 2.1, 22.5, 6.2, 11.4, 12.7
Fifty undergraduate students were randomly selected, and 31 favored a summer externship be provided in their major field of study. At α = 0.05 test the hypothesis that more than 50% of the students favor summer externships for their major field of study.
Rank each set of data.11.7, 18.6, 41.7, 11.7, 16.2, 5.1, 31.4, 5.1, 14.3
A lottery outlet owner hypothesizes that she sells 200 lottery tickets a day. She randomly sampled 40 days and found that on 15 days she sold fewer than 200 tickets. At α = 0.05, is there sufficient evidence to conclude that the median is below 200 tickets?
Six new hybrid automobiles were rated by a consumer group and an independent testing lab. The scale consisted of 1 to 20 points. Is there a relationship between the ratings at α = 0.10? B A Automobile Consumer group Testing lab D E 17 6. 12 11 15 20 18 13 2 19
After reviewing 7 potential textbooks, an instructor ranked them from 1 to 7, with 7 being the highest ranking. The instructor selected one of his previous students and had the student rank the potential textbooks. The rankings are shown. At α = 0.05, is there a relationship between
Two groups of employees were given a questionnaire to assess their degree of satisfaction with their jobs. The questionnaire scores range from 0 to 100. The groups are divided according to years of service. The data are shown. At α = 0.10, can you conclude that there is a difference
Rank each set of data.22, 56, 54, 12, 73, 38, 44, 56, 22, 50, 62, 88
A professor examined a random selection of mathematics research papers to see if there was a relationship between the number of pages in the paper and the number of resources cited in the bibliography. Using the Spearman rank coefficient of correlation, test for a relationship at α =
A group of compulsive gamblers was selected. The amounts (in dollars) they spent on lottery tickets for one week are shown. Then they were required to complete a workshop showing that the chances of winning were not in their favor. After they complete the workshop, test the claim that, at
Students in Greek organizations at schools throughout the country sent volunteers to a yearly blood drive. The numbers from each randomly selected participating school are listed. Test the claim that there is no difference in the number of students participating from fraternities and sororities at
Rank each set of data.88.3, 46.0, 83.4, 321.0, 58.6, 16.0, 148.3, 32.7, 62.8
The scoring leaders for the last 28 years of the NBA are shown below, where E is the Eastern Conference and W is the Western Conference. Test for randomness at α = 0.05. WE W W Ww E E W W E E E E E W E E E E E E W E E E E E E
The prices for 30-count packages of randomly selected store-brand vitamin/mineral supplements are listed from three different sources. At the 0.01 level of significance, can a difference in prices be concluded? Grocery store Discount store Drugstore 6.79 7.49 6.89 7.69 6.09 5.49 7.99 6.10 8.19 6.19
A bookstore owner records the 48 books purchased by customers. He classifies them as either fiction (F) or nonfiction (N). (Read from left to right across each row, and then proceed to the next row.) At α = 0.10, does the typical book purchased occur at random? F F N N N N N N F N N N
A researcher read that the median age for viewers of the Jimmy Fallon show is 52.7 years. To test the claim, 75 randomly selected viewers were surveyed, and 27 were under the age of 52.7. At α = 0.05, test the claim. Give one reason why an advertiser might like to know the results of this study.
Eight randomly selected volunteers at a bowling alley were asked to bowl three games and pick their best score. They were then given a bowling ball made of a new composite material and were allowed to practice with the ball as much as they wanted. The next day they each bowled three games with the
A study was conducted to see if a set of exercises would reduce the number of times a person visits a physical therapist. Eight subjects were selected, and the number of times over a three month period that they visited a physical therapist was recorded. They were then given the exercise program,
A popular amusement park charges a daily admission price that includes all rides. At the end of summer they sponsor a series of nightly parades featuring high school bands from the tristate area. A spectator admission, substantially less than the standard one, is available for people who just want
Ten college students were selected and asked how many soft drinks they drink over a two week period. These students were asked to replace some of the soft drinks with water in order to cut down on the amount of soft drinks that they consumed. At α = 0.10, was there a decrease in the
A stockbroker observes whether the market goes up (U) or down (D) over a 30-day period. The sequence is shown. At α = 0.05, test for randomness.U U U U D D U U U D U U U U U D D D U D
The confidence interval for the median of a set of values less than or equal to 25 in number can be found by ordering the data from smallest to largest, finding the median, and using Table J. For example, to find the 95% confidence interval of the true median for 17, 19, 3, 8, 10, 15, 1, 23, 2, 12,
The confidence interval for the median of a set of values less than or equal to 25 in number can be found by ordering the data from smallest to largest, finding the median, and using Table J. For example, to find the 95% confidence interval of the true median for 17, 19, 3, 8, 10, 15, 1, 23, 2, 12,
The gender of the patients at a medical center is recorded. Test the claim at α = 0.05 that they are admitted at random. м мм м M F F F M M M M M M F M F M м M м м F F F F F M MMMME 2иZL
A marketing student hypothesized that the median price for a 12-inch pepperoni pizza is $9.00. A random selection of 30 restaurants within a 30-mile radius indicated the following prices for a 12-inch pepperoni pizza. Test the claim that the median price is not over 9.00 at α = 0.05.
A police chief records the gender of the drivers who receive speeding tickets. Test the claim at α = 0.05 that the gender of the ticketed drivers is random. MMMMM MMMFM MMFMF
The people who went to the emergency room at a local hospital were treated for an accident (A) or illness (I). Test the claim α = 0.10 that the reason given occurred at random. A A A A. A. A I A A A. A A. A. A A A A I A A I A I A AAIAAA
An instructor wishes to see if the answers to his true/false final exam are random. The answers are shown. Test the claim at α = 0.05.F F T T T F F F T F T T F F FF T T F F T T F F F T F T T T
Find the critical r value for each (assume that the test is two-tailed).n = 50, α = 0.05
Find the critical r value for each (assume that the test is two-tailed).n = 35, α = 0.02
Find the critical r value for each (assume that the test is two-tailed).n = 40, α = 0.01
What is the parametric equivalent test for the Wilcoxon rank sum test?
What are the minimum sample sizes for the Wilcoxon rank sum test?
A large school district has several middle schools. Three schools were randomly chosen, and four classes were selected from each. The numbers of pupils in each class are shown here. At α = 0.10, is there sufficient evidence that the mean number of students per class differs among
The data show the particulate matter in micrograms per cubic meter for a sample of large cities on three continents. At α = 0.10, is there a difference in the mean particulate matter among these continents? Asia Europe North America 21 27 83 24 46 36 118 34 54 154 27 17 50 22 16 42
To compare two means after a significant F test, the Scheffé test and the Tukey test were shown. Another commonly used test is called the Bonferroni multiple-comparison test. This test uses the t distribution, but unlike the t test shown in Chapters 8 and 9, the critical value is
The number of grams of fiber per serving for a random sample of three different kinds of foods is listed. Is there sufficient evidence at the 0.05 level of significance to conclude that there is a difference in mean fiber content among breakfast cereals, fruits, and vegetables? Chocolate Candy
The data shown are the weekly admissions, in millions, of people attending movie theaters over three different time periods. At α = 0.05, is there a difference in the means for the weekly attendance for these time periods? 1950–1974 1975–1990 1991–2000 58.0 17.1 23.3 39.9 19.9
The sales in millions of dollars for a year of a sample of leading companies are shown. At α = 0.01, is there a significant difference in the means? Chocolate Candy Cereal Coffee 578 311 261 320 106 185 264 109 302 249 125 689 237 173
Hands-on soap bubble experiments are a great way to teach mathematics. In an effort to find the best possible bubble solution, two different soap concentrations were used along with two different amounts of glycerin additive. Students were then given a flat glass plate and a straw and were asked to
Fractures accounted for 2.4% of all U.S. emergency room visits for a total of 389,000 visits for a recent year. A random sample of weekly ER visits is recorded for three hospitals in a large metropolitan area during the summer months. At α = 0.05, is there sufficient evidence to
When can the main effects for the two-way ANOVA be interpreted independently?
The CO2emissions in metric tons for selected countries are shown for selected years. At α = 0.10, is there a difference in the means for the selected years? 1990 1980 2000 2010 291.2 578.6 991.0 564.6 202.1 468.7 131.7 321.5 290.5 613.6 470.6 451.0 235.0 302.2 560.3 414.5 198.8 415.4
What are the two types of interactions that can occur in the two-way ANOVA?
The following data show the yearly budgets for leading business sectors in the United States. At α = 0.05, is there a significant difference in the mean budgets of the business sectors? The data are in thousands of dollars. Food Supportive services Beverages Electronics producers 170
When there is no significant difference among three or more means, the value of F will be close to what number?
How are the F test values computed?
Define between-group variance and within-group variance.
How are the values for the mean squares computed?
Explain what is meant by main effects and interaction effect.
Explain the difference between the two tests used to compare two means when the null hypothesis is rejected using the one-way ANOVA F test.
How does the two-way ANOVA differ from the oneway ANOVA?
What two tests can be used to compare two means when the null hypothesis is rejected using the one-way ANOVA F test?
What test is used to compare three or more means?
A study was done on people convicted of using illegal drugs and their ages. The data are shown. At α = 0.10, test the claim that the proportions of the type of drug used are the same for the three age groups. Inhalants Hallucinogens Tranquilizers Age 12-17 18–25 26 and older 16 22
A study was done using a sample of 60 college athletes and 60 college students who were not athletes. They were asked their meat preference. The data are shown. At α = 0.05, test the claim that the preference proportions are the same. Beef 36 28 Pork Poultry Athletes Nonathletes 15 17
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