Concept explainers
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 |
- a. How large was the sample in this survey?
- 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.
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
Actress | Age 18-30 | Age 31-44 | Age 45-58 | Age over 58 | Total |
Jessica Chastain | 51 | 50 | 41 | 42 | 184 |
Jennifer Lawrence | 63 | 55 | 37 | 50 | 205 |
Emmanuelle Riva | 15 | 44 | 56 | 74 | 189 |
Quvenzhane Wallis | 48 | 25 | 22 | 31 | 126 |
Naomi Watts | 36 | 65 | 62 | 33 | 196 |
Total | 213 | 239 | 218 | 230 | 900 |
Thus, the sample size is 900.
b.
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,
The sample proportion of movie fan for Jennifer Lawrence is,
The sample proportion of movie fan for Emmanuelle Riva is,
The sample proportion of movie fan for Quvenzhane Wallis is,
The sample proportion of movie fan for Naomi Watts is,
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.
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:
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:
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:
Actress | Age 18-30 | Age 31-44 | Age 45-58 | Age over 58 | Total |
Jessica Chastain | 51 | 50 | 41 | 42 | 184 |
Jennifer Lawrence | 63 | 55 | 37 | 50 | 205 |
Emmanuelle Riva | 15 | 44 | 56 | 74 | 189 |
Quvenzhane Wallis | 48 | 25 | 22 | 31 | 126 |
Naomi Watts | 36 | 65 | 62 | 33 | 196 |
Totals | 213 | 239 | 218 | 230 | 900 |
The formula for expected frequency is given below:
The expected frequency for each category is calculated as follows:
Actress | Age 18-30 | Age 31-44 | Age 45-58 | Age over 58 |
Jessica Chastain | ||||
Jennifer Lawrence | ||||
Emmanuelle Riva | ||||
Quvenzhane Wallis | ||||
Naomi Watts |
The formula for chi-square test statistic is given as,
The value of chi-square test statistic is,
Thus, the chi-square test statistic is 77.74.
Degrees of freedom:
The degrees of freedom are
In the given problem
Therefore,
Level of significance:
The given level of significance is
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:
From the MINITAB output, the p-value is 0.
Rejection rule:
If the
Conclusion:
Here, the p-value is less than the level of significance.
That is,
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?
Chapter 12 Solutions
Bundle: Statistics for Business & Economics, Loose-leaf Version, 13th + MindTap Business Statistics with XLSTAT, 2 terms (12 months) Printed Access Card
- 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, 277 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 α = 0.05. State the null and alternative hypothesis. (Enter != for ≠ as needed.) H0: p≤0.79 Ha: p>0.79 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…arrow_forwardA survey of 300 workers yielded the following information: 231 workers belonged to a union and 195 were Democrats. If 172 of the union members were Democrats, how many workers were neither belonged to a union nor were Democrats?arrow_forwardA company conducted a marketing survey of its clientele and found that 215 own an iPhone and 106 own an iPad. If 19 clients own both an iPhone and an iPad, how many interviewed have an iPhone or an iPad?arrow_forward
- In one year, three awards (research, teaching, and service) will be given to a class of 25 graduate students in a statistics department. If each student can receive at most one award, how many possible selections are there?arrow_forwardAn industrial/organizational psychologist wants to improve worker productivity for a client firm, but first he needs to gain a better understanding of the life of the typical white-collar professional. Fortunately, he has access to the 2008 Workplace Productivity Survey, commissioned by LexisNexis and prepared by WorldOne Research, which surveyed a sample of 650 white-collar professionals (250 legal professionals and 400 other professionals). One of the survey questions was, “How many hours do you work at your job on a typical workday?” For the subsample of legal professionals (n = 250), the mean response was M = 9.0 hours, with a sample standard deviation of s = 10.4 hours. The estimated standard error is sMM = . Use the following Distributions tool to develop a 99% confidence interval estimate of the mean number of hours legal professionals work on a typical workday. The psychologist can be 99% confident that the interval from to includes the unknown…arrow_forwardAccording 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, 279 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…arrow_forward
- A small ice cream parlor has had great success over the past several years and is interested in expanding into handmade chocolate candies. A poll of 56 randomly selected customers was asked if they would purchase these chocolate candies. Forty of the customers indicated that they would.arrow_forwardAccording to Inc.com, 71% 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.arrow_forwardThe Party of Nonvoters From past elections, nonvoters are those who are either not registered to vote or are considered unlikely to vote in an upcoming election. Nonvoters are very different demographically from likely voters.Nonvoters are more racially and ethnically diverse. 43% of those who are not likely to cast a ballot are Hispanic, African or other racial and ethnic minorities, roughly double the percentage amoung likely voters(22%) (Source: Pew Research Center, October, 2014, "The Party of Nonvoters"). Suppose you interview 10 people who are considered nonvoters. Round answers to 4 decimal places.a.) What is the probability that 5 of them are an ethnic minority? b.) What is the probability that more than 8 are an ethnic minority? c.) What is the probability that at least 8 are not an ethnic minority? d.) What is the probability that fewer than 5 are not an ethnic minority?arrow_forward
- 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 308 of the 370 respondents use social media in their job search. In addition, 283 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 α = 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…arrow_forwardFor the purposes of a marketing research, a survey of 1000 women is conducted in a town. The results show that 52 % liked watching comedies, 45% liked watching fantasy movies and 60% liked watching romantic movies. In addition, 25% liked watching comedy and fantasy both, 28% liked watching romantic and fantasy both and 30% liked watching comedy and romantic movies both. 6% liked watching none of these movie genres. Find The number of women who like watching at least two of the given genresarrow_forwardThe Census Bureau Web site gives several choices for "average income" in its historical income data. In 2006, the median income of American households was $48,201. The mean household income was $66,570. The median income of families was $58,407, and the mean family income was $77,315. The Census Bureau says, “Households consist of all people who occupy a housing unit. The term ‘family’ refers to a group of two or more people related by birth, marriage, or adoption who reside together.” Identify the reason for mean incomes for households being higher than median incomes for households.arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman