• Home
  • Textbooks
  • Statistics for Business Economics
  • Nonparametric Methods

Statistics for Business Economics

David R. Anderson, Dennis J. Sweeney, Thomas A. Williams

Chapter 19

Nonparametric Methods - all with Video Answers

Educators

Chapter Questions

01:05

Problem 1

The following hypothesis test is to be conducted.
\[\begin{array}{l}H_{0}: \text { Median } \geq 150 \\H_{\mathrm{a}}: \text { Median }<150\end{array}\]
A sample of 30 provided 22 observations greater than 150,3 observations equal to 150 and 5 observations less than $150 .$ Use $\alpha=.01 .$ What is your conclusion?

Dominador Tan
Dominador Tan
Numerade Educator
00:21

Problem 2

Ten individuals participated in a taste test involving two brands of a product. Sample results show 7 preferred brand $A, 2$ preferred brand $B,$ and 1 was unable to state a preference. With $\alpha=.05,$ test for a significant difference in the preferences for the two brands. What is your conclusion?

Bryan Meares
Bryan Meares
Numerade Educator
00:21

Problem 3

Ten individuals participated in a taste test involving two brands of a product. Sample results show 7 preferred brand $A, 2$ preferred brand $B,$ and 1 was unable to state a preference. With $\alpha=.05,$ test for a significant difference in the preferences for the two brands. What is your conclusion?

Bryan Meares
Bryan Meares
Numerade Educator
01:39

Problem 4

Net assets for the 50 largest stock mutual funds show a median of $\$ 15$ billion (The Wall Street Journal, March 2, 2009). A sample of 10 of the 50 largest bond mutual funds follows.
Using the median, can it be concluded that bond mutual funds are smaller and have fewer net assets than stock mutual funds? Use $a=.05$
a. What are the hypotheses for this test?
b. What is the $p$ -value? What is your conclusion?

Nick Johnson
Nick Johnson
Numerade Educator
05:55

Problem 5

The median annual income of subscribers to Shutterbug magazine is $\$ 75,000$ (Home Theater website, August 18,2008 ). A sample of 300 subscribers to Popular Photography \& Imaging magazine found 165 subscribers with an annual income over $\$ 75,000$ and 135 with an annual income under $\$ 75,000$. Can you conclude that the median annual income of Popular Photography \& Imaging subscribers differs from the median annual income of Shutterbug subscribers? Use $\alpha=.05$

Neel Faucher
Neel Faucher
Numerade Educator
05:55

Problem 6

The median annual income for families living in the United States is $\$ 56,200$ (The New York Times Almanac, 2008 ). Annual incomes in thousands of dollars for a sample of 50 families living in Chicago, Illinois, are shown. Use the sample data to see if it can be concluded that the families living in Chicago have a median annual income greater than $\$ 56,200 .$ Use $\alpha=.05 .$ What is your conclusion?

Neel Faucher
Neel Faucher
Numerade Educator
02:35

Problem 7

Are stock splits beneficial to stockholders? SNL Financial studied stock splits in the banking industry over an 18 -month period. For a sample of 20 stock splits, 14 led to an increase in investment value, 4 led to a decrease in investment value, and 2 resulted in no change. Conduct a sign test to determine if it can be concluded that stock splits are beneficial for holders of bank stocks.
a. What are the null and alternative hypotheses?
b. $\quad$ Using $\alpha=.05,$ what is your conclusion?

Nick Johnson
Nick Johnson
Numerade Educator
08:41

Problem 8

A Pew Rescarch Center survey asked adults if their ideal place to live would have a faster pace of life or a slower pace of life (USA Today, February 13,2009 ). A preliminary sample of 16 respondents showed 4 preferred a faster pace of life, 11 preferred a slower place of life, and 1 said it did not matter.
a. Are these data sufficient to conclude there is a difference between the preferences for a faster pace of life or a slower pace of life? Use $\alpha=.05 .$ What is your conclusion?
b. Considering the entire sample of 16 respondents, what is the percentage who would like a faster pace of life? What is the percentage who would like a slower pace of life? What recommendation do you have for the study?

Srikar Katta
Srikar Katta
Numerade Educator
04:22

Problem 9

A poll taken during the recession in 2008 asked 600 adults a series of questions about the state of the economy and their children's future. One question was, "Do you expect your children to have a better life than you have had, a worse life, or a life about the same as yours?" The responses showed 242 better, 310 worse, and 48 about the same. Use the sign test and $\alpha=.05$ to determine whether there is a difference between the number of adults who feel their children will have a better life compared to a worse life. What is your conclusion?

Neel Faucher
Neel Faucher
Numerade Educator
05:57

Problem 10

Nielsen Media Research identified American Idol and Dancing with the Stars as the two top-rated prime-time television shows (USA Today, April 14, 2008). In a local television preference survey, 750 individuals were asked to indicate their favorite prime-time television show: Three hundred thirty selected American Idol, 270 selected Dancing with the Stars, and 150 selected another television show. Use a .05 level of significance to test the hypothesis that there is no difference in the preference for the American Idol and Dancing with the Stars television shows. What is your conclusion?

Mihir Nayar
Mihir Nayar
Numerade Educator
14:45

Problem 11

Competition in the personal computer market is intense. A sample of 450 purchases showed 202 Brand $A$ computers, 175 Brand $B$ computers, and 73 other computers. Use a .05 level of significance to test the null hypothesis that Brand $\mathrm{A}$ and $\mathrm{Brand} \mathrm{B}$ have the same share of the personal computer market. What is your conclusion?

Evelyn Cunningham
Evelyn Cunningham
Numerade Educator
10:34

Problem 12

Two fuel additives are tested to determine their effect on miles per gallon for passenger cars. Test results for 12 cars follow; each car was tested with both fuel additives. Use $\alpha=.05$ and the Wilcoxon signed-rank test to see whether there is a significant difference between the median miles per gallon for the additives.

Paul A.
Paul A.
California State Polytechnic University, Pomona
02:28

Problem 13

A sample of 10 men was used in a study to test the effects of a relaxant on the time required to fall asleep. Data for 10 subjects showing the number of minutes required to fall asleep with and without the relaxant follow. Use a .05 level of significance to determine whether the relaxant reduces the median time required to fall asleep. What is your conclusion?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
05:56

Problem 14

Percents of on-time arrivals for flights in 2006 and 2007 were collected for 11 randomly selected airports. Data for these airports follow (Research and Innovative Technology Administration website, August 29,2008 ). Use $\alpha=.05$ to test the hypothesis that there is no difference between the median percent of on-time arrivals for the two years. What is your conclusion?

Wendi Obritz
Wendi Obritz
Numerade Educator
01:54

Problem 15

A test was conducted for two overnight mail delivery services. Two samples of identical deliveries were set up so that both delivery services were notified of the need for a delivery at the same time. The hours required to make each delivery follow. Do the data shown suggest a difference in the median delivery times for the two services? Use a .05 level of significance for the test.

Akhil Choudhary
Akhil Choudhary
Numerade Educator
03:11

Problem 16

The PGA Players Championship was held at the Sedgefield Country Club in Greensboro, North Carolina, August $11-17,2008$. Shown here are first-round and second-round scores for a random sample of 11 golfers. Use $\alpha=.05$ to determine whether the first- and second-round median scores for golfers in the Players Championship differed significantly. What is your conclusion?

Jon Southam
Jon Southam
Numerade Educator
07:51

Problem 17

The Scholastic Aptitude Test (SAT) consists of three parts: critical reading, mathematics, and writing. Each part of the test is scored on a 200 - to 800 -point scale with a median of approximately 500 (The World Almanac, 2009 ). Scores for each part of the test can be assumed to be symmetric. Use the following data to test the hypothesis that the population median score for the students taking the writing portion of the SAT is $500 .$ Using $\alpha=.05$ what is your conclusion?

Vaidik Stats
Vaidik Stats
Numerade Educator
10:34

Problem 18

Two fuel additives are being tested to determine their effect on gasoline mileage. Seven cars were tested with additive 1 and nine cars were tested with additive $2 .$ The following data show the miles per gallon obtained with the two additives. Use $\alpha=.05$ and the MWW test to see whether there is a significant difference between gasoline mileage for the two additives.

Paul A.
Paul A.
California State Polytechnic University, Pomona
10:34

Problem 18

Two fuel additives are being tested to determine their effect on gasoline mileage. Seven cars were tested with additive 1 and nine cars were tested with additive $2 .$ The following data show the miles per gallon obtained with the two additives. Use $\alpha=.05$ and the MWW test to see whether there is a significant difference between gasoline mileage for the two additives.

Paul A.
Paul A.
California State Polytechnic University, Pomona
06:36

Problem 19

Samples of starting annual salaries for individuals entering the public accounting and financial planning professions follow. Annual salaries are shown in thousands of dollars.
a. Use a .05 level of significance and test the hypothesis that there is no difference between the starting annual salaries of public accountants and financial planners. What is your conclusion?
b. What are the sample median annual salaries for the two professions?

Sneha Ravi
Sneha Ravi
Numerade Educator
03:26

Problem 20

The gap between the earnings of men and women with equal education is narrowing but has not closed. Sample data for seven men and seven women with bachelor's degrees are as follows. Data are shown in thousands of dollars.$\begin{array}{ll}\text { Men } & \text { Women } \\ 35.6 & 49.5 \\ 80.5 & 40.4 \\ 50.2 & 32.9 \\ 67.2 & 45.5 \\ 43.2 & 30.8 \\ 54.9 & 52.5 \\ 60.3 & 29.8\end{array}$
a. What is the median salary for men? For women?
b. Use $a=.05$ and conduct the hypothesis test for identical population distributions. What is your conclusion?

Jameson Kuper
Jameson Kuper
Numerade Educator
04:19

Problem 21

Unisys maintains a hurricane database which provides information on hurricanes in the Atlantic/Caribbean/Gulf of Mexico and the Eastern Pacific Ocean. Maximum wind speeds in knots for a sample of hurricanes over the past four hurricane seasons are shown (Unisys weather website, April 2009 ).
Use $a=.05$ and test to determine whether the distribution of hurricane wind speeds is the same for these two regions. What is your conclusion?

Gus Steppen
Gus Steppen
Numerade Educator
05:59

Problem 22

Each year $B u$ siness Week publishes statistics on the world's 1000 largest companies. A company's price/earnings (P/E) ratio is the company's current stock price divided by the latest 12 months' earnings per share. The following table shows the P/E ratios for a sample of 10 Japanese companies and 12 U.S. companies. Is the difference between the P/E ratios for the two countries significant? Use the MWW test and $\alpha=.01$ to support your conclusion.

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator
04:09

Problem 23

Police records show the following numbers of daily crime reports for a sample of days during the winter months and a sample of days during the summer months. Use a .05 level of significance to determine whether there is a significant difference between the winter and summer months in terms of the number of crime reports. What is your conclusion? $\begin{array}{cc}\text { Winter } & \text { Summer } \\ 18 & 28 \\ 20 & 18 \\ 15 & 24 \\ 16 & 32 \\ 21 & 18 \\ 20 & 29 \\ 12 & 23 \\ 16 & 38 \\ 19 & 28 \\ 20 & 18\end{array}$

Raymond Matshanda
Raymond Matshanda
Numerade Educator
05:06

Problem 24

A certain brand of microwave oven was priced at 10 stores in Dallas and 13 stores in $\operatorname{San}$ Antonio. The data follow. Use a .05 level of significance and test whether prices for the microwave oven are the same in the two cities. $\begin{array}{cc}\text { Dallas } & \text { San Antonio } \\ 445 & 460 \\ 489 & 451 \\ 405 & 435 \\ 485 & 479 \\ 439 & 475 \\ 449 & 445 \\ 436 & 429 \\ 420 & 434 \\ 430 & 410 \\ 405 & 422 \\ & 425 \\ & 459 \\ & 430\end{array}$

Raymond Matshanda
Raymond Matshanda
Numerade Educator
02:27

Problem 25

The National Football League (NFL) holds its annual draft of the nation's best college football players in April each year. Prior to the draft, various sporting news services project the players who will be drafted along with the order in which each will be selected. The better players are selected earlier in the draft. For the 2009 draft, the colleges from the Southeastern Conference (SEC) and the Atlantic Coast Conference (ACC) were projected to have the most players who would be selected during the first round (SportProjection website, March 15,2009 ). The player's college and the projected draft position for seven players from each conference are as follows.

Using the projected draft position as an indicator of preference the NFL teams have for the two conferences, use the MWW test to determine if there is any difference between the NFL preferences for players from these two conferences? Use $\alpha=.05 .$ What is the $p$ -value? What is your conclusion?

Nick Johnson
Nick Johnson
Numerade Educator
03:14

Problem 26

A sample of 15 consumers provided the following product ratings for three different products. Five consumers were randomly assigned to test and rate each product. Use the Kruskal-Wallis test and $\alpha=.05$ to determine whether there is a significant difference among the ratings for the products. $\begin{array}{lcc} & \text { Product } & \\ \text { A } & \text { B } & \text { C } \\ \text { 50 } & 80 & 60 \\ 62 & 95 & 45 \\ 75 & 98 & 30 \\ 48 & 87 & 58 \\ 65 & 90 & 57\end{array}$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:58

Problem 27

Three admission test preparation programs are being evaluated. The scores obtained by a sample of 20 people who used the programs provided the following data. Use the KruskalWallis test to determine whether there is a significant difference among the three test preparation programs. Use $\alpha=.05$.
$\begin{array}{ccc} & \text { Program } & \\ \mathbf{A} & \mathbf{B} & \mathbf{C} \\ 540 & 450 & 600 \\ 400 & 540 & 630 \\ 490 & 400 & 580 \\ 530 & 410 & 490 \\ 490 & 480 & 590 \\ 610 & 370 & 620 \\ & 550 & 570\end{array}$

Barath Palanisamy
Barath Palanisamy
Numerade Educator
01:19

Problem 28

Forty-minute workouts of one of the following activities three days a week will lead to a loss of weight. The following sample data show the number of calories burned during $40-$ minute workouts for three different activities. Do these data indicate differences in the amount of calories burned for the three activities? Use a .05 level of significance. What is your conclusion? $\begin{array}{ccc}\text { Swimming } & \text { Tennis } & \text { Cycling } \\ 408 & 415 & 385 \\ 380 & 485 & 250 \\ 425 & 450 & 295 \\ 400 & 420 & 402 \\ 427 & 530 & 268\end{array}$

Eleanor Johnson
Eleanor Johnson
Numerade Educator
02:10

Problem 29

Condé Nast Traveler magazine conducts an annual survey of its readers in order to rate the top 80 cruise ships in the world (Condé Nast Traveler, February 2008 ). With 100 the highest possible rating, the overall ratings for a sample of ships from the Holland America, Princess, and Royal Caribbean cruise lines are shown. Use the Kruskal-Wallis test with $\alpha=.05$ to determine whether the overall ratings among the three cruise lines differ significantly, What is your conclusion?

Kari Hasz
Kari Hasz
Numerade Educator
View

Problem 30

A large corporation sends many of its first-level managers to an off-site supervisory skills training course. Four different management development centers offer this course. The director of human resources would like to know whether there is a difference among the quality of training provided at the four centers. An independent random sample of five employees was chosen from each training center. The employees were then ranked 1 to 20 in terms of supervisory skills. A rank of 1 was assigned to the employee with the best supervisory skills. The ranks are shown. Use $a=.05$ and test whether there is a significant difference among the quality of training provided by the four programs.

Victor Salazar
Victor Salazar
Numerade Educator
02:58

Problem 31

The better-selling candies are often high in calories. Assume that the following data show the caloric content from samples of M\&M's, Kit Kat, and Milky Way II. Test for significant differences among the calorie content of these three candies. At a .05 level of significance, what is your conclusion?
$\begin{array}{ccc}\text { M\&M's } & \text { Kit Kat } & \text { Milky Way II } \\ 230 & 225 & 200 \\ 210 & 205 & 208 \\ 240 & 245 & 202 \\ 250 & 235 & 190 \\ 230 & 220 & 180\end{array}$

James Kiss
James Kiss
Numerade Educator
15:35

Problem 32

Consider the following set of rankings for a sample of 10 elements.

a. Compute the Spearman rank-correlation coefficicnt for the data.
b. Use $\alpha=.05$ and test for significant rank correlation. What is your conclusion?

Evelyn Cunningham
Evelyn Cunningham
Numerade Educator
15:35

Problem 33

Consider the following two sets of rankings for six items.
Note that in the first case the rankings are identical, whereas in the second case the rankings are exactly opposite. What value should you expect for the Spearman rank-correlation coefficient for each of these cases? Explain. Calculate the rank-correlation coefficient for each case.

Evelyn Cunningham
Evelyn Cunningham
Numerade Educator
03:27

Problem 34

The following data show the rankings of 11 states based on expenditure per student (ranked 1 highest to 11 lowest ) and student-teacher ratio (ranked 1 lowest to 11 highest).
$\begin{array}{lcc}\text { State } & \text { Fxpenditure per Student } & \text { Student-Teacher Ratio } \\ \text { Arizona } & 9 & 10 \\ \text { Colorado } & 5 & 8 \\ \text { Florida } & 4 & 6 \\ \text { Idaho } & 2 & 11 \\ \text { lowa } & 6 & 4 \\ \text { Louisiana } & 11 & 3 \\ \text { Massachusetts } & 1 & 1 \\ \text { Nebraska } & 7 & 2 \\ \text { North Dakota } & 8 & 7 \\ \text { South Dakota } & 10 & 5 \\ \text { Washington } & 3 & 9\end{array}$
a. What is the rank correlation between expenditure per student and student-teacher ratio. Discuss.
b. $\quad$ At the $\alpha=.05$ level, does there appear to be a relationship between expenditure per student and student-teacher ratio?

Trinity Steen
Trinity Steen
Numerade Educator
02:36

Problem 35

A national study by Harris Interactive, Inc., evaluated the top technology companies and their reputations. The following shows how 10 technology companies ranked in reputation and how the companies ranked in percentage of respondents who said they would purchase the company's stock. A positive rank correlation is anticipated because it seems reasonable to expect that a company with a higher reputation would have the more desirable stock to purchase.
a. Compute the rank correlation between reputation and stock purchase.
b. Test for a significant positive rank correlation. What is the $p$ -value?
c. $\quad$ At $\alpha=.05,$ what is your conclusion?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:15

Problem 36

The rankings of a sample of professional golfers in both driving distance and putting are shown. What is the rank correlation between driving distance and putting for these golfers? Test for significance of the correlation coefficient at the .10 level of significance.$\begin{array}{lcc}\text { Golfer } & \text { Driving Distance } & \text { Putting } \\ \text { Fred Couples } & 1 & 5 \\ \text { David Duval } & 5 & 6 \\ \text { Ernic Els } & 4 & 10 \\ \text { Nick Faldo } & 9 & 2 \\ \text { Tom Lehman } & 6 & 7 \\ \text { Justin Leonard } & 10 & 3 \\ \text { Davis Love III } & 2 & 8 \\ \text { Phil Mickelson } & 3 & 9 \\ \text { Greg Norman } & 7 & 4 \\ \text { Mark O'Meara } & 8 & 1\end{array}$

Tyler Moulton
Tyler Moulton
Numerade Educator
03:21

Problem 37

A student organization surveyed both current students and recent graduates to obtain information on the quality of teaching at a particular university. An analysis of the responses provided the following teaching-ability rankings. Do the rankings given by the current students agree with the rankings given by the recent graduates? Use $a=.10$ and test for a significant rank correlation.
$\begin{array}{ccc}\text { Professor } & \text { Current Students } & \text { Recent Graduates } \\ 1 & 4 & 6 \\ 2 & 6 & 8 \\ 3 & 8 & 5 \\ 4 & 3 & 1 \\ 5 & 1 & 2 \\ 6 & 2 & 3 \\ 7 & 5 & 7 \\ 8 & 10 & 9 \\ 9 & 7 & 4 \\ 10 & 9 & 10\end{array}$

Trent Speier
Trent Speier
Numerade Educator
01:17

Problem 38

A survey asked the following question: Do you favor or oppose providing tax-funded vouchers or tax deductions to parents who send their children to private schools? Of the 2010 individuals surveyed, 905 favored the proposal, 1045 opposed the proposal, and 60 offered no opinion, Do the data indicate a significant difference in the preferences for the financial support of parents who send their children to private schools? Use a .05 level of significance.

James Kiss
James Kiss
Numerade Educator
03:27

Problem 39

Due to a recent decline in the housing market, the national median sales price for singlefamily homes is $\$ 180,000$ (The National Association of Realtors, January 2009 ). Assume that the following data were obtained from samples of recent sales of single-family homes in St. Louis and Denver.
a. Is the median sales price in St. Louis significantly lower than the national median of $\$ 180,000 ?$ Use a statistical test with $a=.05$ to support your conclusion.
b. Is the median sales price in Denver significantly higher than the national median of $\$ 180,000 ?$ Use a statistical test with $\alpha=.05$ to support your conclusion.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
04:02

Problem 40

Twelve homemakers were asked to estimate the retail selling price of two models of refrigerators. Their estimates of selling price are shown in the following table. Use these data and test at the .05 level of significance to determine whether there is a difference between the two models in terms of homemakers' perceptions of selling price.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
03:46

Problem 41

A study was designed to evaluate the weight-gain potential of a new poultry feed. A sample of 12 chickens was used in a six-week study. The weight of each chicken was recorded before and after the six-week test period. The differences between the before and after weights of the 12 chickens are as follows: $1.5,1.2,-.2, .0, .5, .7, .8,1.0, .0, .6, .2,-.01 . A$ positive difference indicates a weight gain and a negative difference indicates a weight loss. Use a .05 level of significance to determine if the new feed provides a significant weight gain for the chickens.

James Kiss
James Kiss
Numerade Educator
02:07

Problem 42

The following data are product weights for the same items produced on two different production lines. Test for a difference between the product weights for the two lines. Use $\alpha=.05$. $\begin{array}{ll}\text { Line } 1 & \text { Line } 2 \\ 13.6 & 13.7 \\ 13.8 & 14.1 \\ 14.0 & 14.2 \\ 13.9 & 14.0 \\ 13.4 & 14.6 \\ 13.2 & 13.5 \\ 13.3 & 14.4 \\ 13.6 & 14.8 \\ 12.9 & 14.5 \\ 14.4 & 14.3 \\ & 15.0 \\ & 14.9\end{array}$

Ethan Dotson-Kelly
Ethan Dotson-Kelly
Numerade Educator
01:04

Problem 43

A client wants to determine whether there is a significant difference in the time required to complete a program evaluation with the three different methods that are in common use. The times (in hours) required for each of 18 evaluators to conduct a program evaluation follow. Use $\alpha=.05$ and test to see whether there is a significant difference in the time required by the three methods. $\begin{array}{ccc}\text { Method 1 } & \text { Method 2 } & \text { Method 3 } \\ 68 & 62 & 58 \\ 74 & 73 & 67 \\ 65 & 75 & 69 \\ 76 & 68 & 57 \\ 77 & 72 & 59 \\ 72 & 70 & 62\end{array}$

Shu Naito
Shu Naito
Numerade Educator
01:52

Problem 44

A sample of 20 engineers employed with a company for three years has been rank ordered with respect to managerial potential. Some of the engineers attended the company's management-development course, others attended an off-site management-development program at a local university, and the remainder did not attend any program. Use the following rankings and $\alpha=.025$ to test for a significant difference in the managerial potential of the three groups. $\begin{array}{ccc}\text { No Program } & \text { Company Program } & \text { Off-Site Program } \\ 16 & 12 & 7 \\ 9 & 20 & 1 \\ 10 & 17 & 4 \\ 15 & 19 & 2 \\ 11 & 6 & 3 \\ 13 & 18 & 8 \\ & 14 & 5\end{array}$

Adriano Chikande
Adriano Chikande
Numerade Educator
03:17

Problem 45

Course evaluation ratings for four college instructors are shown in the following table. Use $\alpha=.05$ and test for a significant difference among the rating for these instructors. What is your conclusion?

Raymond Matshanda
Raymond Matshanda
Numerade Educator
04:51

Problem 46

A sample of 15 students received the following rankings on midterm and final examinations in a statistics course. Compute the Spearman rank-correlation coefficient for the data and test for a significant correlation with $\alpha=.10 .$ What is the $p$ -value and what is your conclusion?

Raymond Matshanda
Raymond Matshanda
Numerade Educator
05:57

Problem 47

Nielsen Research provides weekly ratings of nationally broadcast television programs. The ratings of the 84 prime-time programs broadcast by the four major televisions networks $(\mathrm{ABC},$ $\mathrm{CBS}, \mathrm{FOX},$ and $\mathrm{NBC}$, for the week of April $14-20,2008,$ are provided in the file named NielsenResearch. The ratings range from 1 to $103 .$ Shown are the ratings for 12 shows in the file (days and times for shows that aired multiple episodes are shown). Do these data suggest that the overall ratings for the four networks differ significantly? Use the Kruskal-Wallis test with a .10 level of significance. What is the $p$ -value and what is your conclusion?

Mihir Nayar
Mihir Nayar
Numerade Educator