Bundle: Statistics for Business & Economics, Loose-leaf Version, 13th + MindTap Business Statistics with XLSTAT, 2 terms (12 months) Printed Access Card
Bundle: Statistics for Business & Economics, Loose-leaf Version, 13th + MindTap Business Statistics with XLSTAT, 2 terms (12 months) Printed Access Card
13th Edition
ISBN: 9781337127264
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 12.2, Problem 16E

The race for the 2013 Academy Award for Actress in a Leading Role was extremely tight, featuring several worthy performances (ABC News online, February 22, 2013). The nominees were Jessica Chastain for Zero Dark thirty, Jennifer Lawrence for Silver Linings Playbook, Emmanuelle Riva for Amour, Quvenzhané Wallis for Beasts of the Southern Wild, and Naomi Watts for the Impossible. In a survey, movie fans who had seen each of the movies for which these five actresses had been nominated were asked to select the actress who was most deserving of the 2013 Academy Award for Actress in a Leading Role. The responses follow.

18–30 31–4 45–58 Over 58
Jessica Chastain 51 50 41 42
Jennifer Lawrence 63 55 37 50
Emmanuelle Riva 15 44 56 74
Quvenzhané Wallis 48 25 22 31
Naomi Watts 36 65 62 33
  1. a. How large was the sample in this survey?
  2. b. Jennifer Lawrence received the 2013 Academy Award for Actress in a Leading Role for her performance in Silver Linings Playbook. Did the respondents favor Ms. Lawrence? c. at α = .05, conduct a hypothesis test to determine whether people’s attitude toward the actress who was most deserving of the 2013 Academy Award for Actress in a Leading Role is independent of respondent age. What is your Conclusion?

a.

Expert Solution
Check Mark
To determine

Find the sample size for the given survey.

Answer to Problem 16E

The sample size is 900.

Explanation of Solution

Calculation:

The given observed frequency (fij) as the row and column total is tabulated below:

ActressAge 18-30Age 31-44Age 45-58Age over 58Total
Jessica Chastain51504142184
Jennifer Lawrence63553750205
Emmanuelle Riva15445674189
Quvenzhane Wallis48252231126
Naomi Watts36656233196
Total213239218230900

Thus, the sample size is 900.

b.

Expert Solution
Check Mark
To determine

Explain whether the respondents favor Ms. Lawrence.

Explanation of Solution

Calculation:

Jennifer Lawrence received the 2013 Academy Award for actress in a leading role for “Silver Lining Playbook”.

The sample proportion of movie fan for Jessica Chastain is,

p1¯=184900=0.2044

The sample proportion of movie fan for Jennifer Lawrence is,

p2¯=205900=0.2278

The sample proportion of movie fan for Emmanuelle Riva is,

p3¯=189900=0.2100

The sample proportion of movie fan for Quvenzhane Wallis is,

p4¯=126900=0.1400

The sample proportion of movie fan for Naomi Watts is,

p5¯=196900=0.2178

It is clear that, the sample proportion for Jennifer Lawrence is highest. Thus, the respondents favor Ms. Lawrence. However, Jessica Chastain, Emmanuelle Riva and Naomi Watts were also favored by almost as many of fans.

c.

Expert Solution
Check Mark
To determine

Perform a hypothesis test to determine whether people’s attitude toward the actress who was most deserving of the 2013 Academy Award for Actress in a Leading Role is independent of respondent age at 5% level of significance and draw conclusion of the study.

Answer to Problem 16E

The data provide sufficient evidence to conclude that people’s attitude toward the actress who was most deserving of the 2013 Academy Award for Actress in a Leading Role is not independent of respondent age.

Explanation of Solution

Calculation:

State the test hypotheses.

Null hypothesis:

 H0:The two cataegorical variables are independent

That is, people’s attitude toward the actress who was most deserving of the 2013 Academy Award for Actress in a Leading Role is independent of respondent age.

Alternative hypothesis:

 Ha:The two cataegorical variables are not independent

That is, people’s attitude toward the actress who was most deserving of the 2013 Academy Award for Actress in a Leading Role is not independent of respondent age.

The row and column total is tabulated below:

ActressAge 18-30Age 31-44Age 45-58Age over 58Total
Jessica Chastain51504142184
Jennifer Lawrence63553750205
Emmanuelle Riva15445674189
Quvenzhane Wallis48252231126
Naomi Watts36656233196
Totals213239218230900

The formula for expected frequency is given below:

eij=(Row i Total)(Coloumn j Total)Total Sample Size

The expected frequency for each category is calculated as follows:

ActressAge 18-30Age 31-44Age 45-58Age over 58
Jessica Chastain(184)(213)900=43.5(184)(239)900=48.9(184)(218)900=44.6(184)(230)900=47
Jennifer Lawrence(205)(213)900=48.5(205)(239)900=54.4(205)(218)900=49.7(205)(230)900=52.4
Emmanuelle Riva(189)(213)900=29.8(189)(239)900=50.2(189)(218)900=45.8(189)(230)900=48.3
Quvenzhane Wallis(126)(213)900=29.8(126)(239)900=33.5(126)(218)900=30.5(126)(230)900=32.2
Naomi Watts(196)(213)900=46.4(196)(239)900=52(196)(218)900=47.5(196)(230)900=50.1

The formula for chi-square test statistic is given as,

χ2=i=1rj=1c(fijeij)2eij where r represent the rth row and c represents the cth column

The value of chi-square test statistic is,

χ2={(5143)243+(5048)248+(4144)244+(4247)247+(6348)248+(5554)254+(3749)249+(5052)252+(1529)229+(4450)250+(5645)245+(7448)248+(4829)229+(2533)233+(2230)230+(3132)232+(3646)246+(6552)252+(6247)247+(3350)250}=(1.28+0.03+0.29+0.54+4.32+0.01+3.23+0.11+19.76+0.76+2.28+13.67+11.08+2.14+2.38+0.04+2.33+3.22+4.44+5.83)=77.74

Thus, the chi-square test statistic is 77.74.

Degrees of freedom:

The degrees of freedom are df=(r1)(c1) for the contingency table of r rows and c columns.

In the given problem r=5 and c=4.

Therefore,

df=(51)(41)=12

Level of significance:

The given level of significance is α=0.05.

p-value:

Software procedure:

Step -by-step software procedure to obtain p-value using MINITAB software is as follows:

  • Select Graph > Probability distribution plot > view probability
  • Select chi-square under distribution and enter 12 in degrees of freedom.
  • Choose X-Value and Right Tail for the region of the curve to shade.
  • Enter the X-value as 77.74 under shaded area.
  • Select OK.
  • Output using MINITAB software is given below:

Bundle: Statistics for Business & Economics, Loose-leaf Version, 13th + MindTap Business Statistics with XLSTAT, 2 terms (12 months) Printed Access Card, Chapter 12.2, Problem 16E

From the MINITAB output, the p-value is 0.

Rejection rule:

If the p-valueα, then reject the null hypothesis.

Conclusion:

Here, the p-value is less than the level of significance.

That is, p-value(=0)<α(=0.05)

Thus, the decision is “reject the null hypothesis”.

Therefore, the data provide sufficient evidence to conclude that column variable is not independent of row variable. That is, there is an association between column and row variable.

Thus, the data provide sufficient evidence to conclude that people’s attitude toward the actress who was most deserving of the 2013 Academy Award for Actress in a Leading Role is not independent of respondent age.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
According to Inc.com, 79% of job seekers used social media in their job search in 2018. Many believe this number is inflated by the proportion of 22- to 30- year-old job seekers who use social media in their job search. A survey of 22- to 30-year-old job seekers showed that 310 of the 370 respondents use social media in their job search. In addition, 275 of the 370 respondents indicated they have electronically submitted a resume to an employer. a. Conduct a hypothesis test to determine if the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that use social media in their job search. Use a = 0.05. Но: р - Select your answer - На: : р - Select your answer - p-value: (to 4 decimals) What is your conclusion? - Select your answer - Но. We - Select your answer - v conclude that the proportion of 22 – 30 year old job seekers that use social media in their job search…
A communications class surveyed 150 students and found that 115 had seen the movie “Titanic” while 65 had seen “Forrest Gump” and 42 had seen both. How many people had not seen either movie?
According to Inc.com, 79% of job seekers used social media in their job search in 2018. Many believe this number is inflated by the proportion of 22- to 30-year-old job seekers who use social media in their job search. Suppose a survey of 22- to 30-year-old job seekers showed that 306 of the 370 respondents use social media in their job search. In addition, 281 of the 370 respondents indicated they have electronically submitted a resume to an employer.   (a)Conduct a hypothesis test to determine if the results of the survey justify concluding the proportion of 22- to 30-year-old job seekers who use social media in their job search exceeds the proportion of the population that use social media in their job search. Use ? = 0.05.   State the null and alternative hypothesis. (Enter != for ≠ as needed.) H0:   Ha:       Find the value of the test statistic. (Round your answer to two decimal places.) =    Find the p-value. (Round your answer to four decimal places.) p-value =    State…

Chapter 12 Solutions

Bundle: Statistics for Business & Economics, Loose-leaf Version, 13th + MindTap Business Statistics with XLSTAT, 2 terms (12 months) Printed Access Card

Ch. 12.2 - A Bloomberg Businessweek subscriber study asked,...Ch. 12.2 - A Deloitte employment survey asked a sample of...Ch. 12.2 - health insurance benefits vary by the size of the...Ch. 12.2 - A vehicle quality survey asked new owners a...Ch. 12.2 - The Wall Street Journal Corporate Perceptions...Ch. 12.2 - The race for the 2013 Academy Award for Actress in...Ch. 12.2 - The national Sleep Foundation used a survey to...Ch. 12.2 - Prob. 18ECh. 12.3 - Test the following hypotheses by using the 2...Ch. 12.3 - The following data are believed to have come from...Ch. 12.3 - During the first 13 weeks of the television...Ch. 12.3 - Mars, Inc. manufactures MMs, one of the most...Ch. 12.3 - The wall street Journals Shareholder Scoreboard...Ch. 12.3 - The national highway Traffic Safety administration...Ch. 12.3 - use = .01 and conduct a goodness of fit test to...Ch. 12.3 - The weekly demand for a product is believed to be...Ch. 12 - In a quality control test of parts manufactured at...Ch. 12 - Phoenix Marketing international identified...Ch. 12 - The five most popular art museums in the world are...Ch. 12 - A Pew Research Center survey asked respondents if...Ch. 12 - Bara Research Group conducted a survey about...Ch. 12 - An ambulance service responds to emergency calls...Ch. 12 - Based on sales over a six-month period, the five...Ch. 12 - A random sample of final examination grades for a...Ch. 12 - A salesperson makes four calls per day. A sample...Ch. 12 - In a study conducted by Zogby International for...
Knowledge Booster
Background pattern image
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Find number of persons in a part with 66 handshakes Combinations; Author: Anil Kumar;https://www.youtube.com/watch?v=33TgLi-wp3E;License: Standard YouTube License, CC-BY
Discrete Math 6.3.1 Permutations and Combinations; Author: Kimberly Brehm;https://www.youtube.com/watch?v=J1m9sB5XZQc;License: Standard YouTube License, CC-BY
How to use permutations and combinations; Author: Mario's Math Tutoring;https://www.youtube.com/watch?v=NEGxh_D7yKU;License: Standard YouTube License, CC-BY
Permutations and Combinations | Counting | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=0NAASclUm4k;License: Standard Youtube License
Permutations and Combinations Tutorial; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=XJnIdRXUi7A;License: Standard YouTube License, CC-BY