Testing Claims about Proportions. In

Problem 1BSC Hypothesis Tests and Confidence Intervals We can test a claim about a population proportion using the P-value method of hypothesis testing or the critical value method of hypothesis testing, or we could base our conclusion on a confidence interval. Assuming that all three methods are based on the same significance level, which two of the three methods always yield the same conclusion?

Problem 2BSC Sample Proportion In a Wakefield Research survey, respondents were asked if they ever hesitated to give a handshake because of a fear of germs. Of the respondents, 411 answered “yes” and 592 said “no.” What is the sample proportion of yes responses, and what notation is used to represent it?

Problem 3BSC P-Value Using the sample data from Exercise, we can test the claim that p < 0.5, where p denotes the proportion of “yes” responses for the population. Some technologies provide results that include a P-value of 5.50E—9. Write that number using ordinary notation. What does the P-value suggest about the claim? Sample Proportion In a Wakefield Research survey, respondents were asked if they ever hesitated to give a handshake because of a fear of germs. Of the respondents, 411 answered “yes” and 592 said “no.” What is the sample proportion of yes responses, and what notation is used to represent it?

Problem 4BSC Notation and P-Value a. Refer to Exercise and distinguish between the value of p and the P-value. ________________ b. In Section 8-2 we noted that we can remember how to interpret P-values with this: “If the P is low, the null must go.” What does this mean? ________________ c. Another memory trick commonly used is this: “If the P is high, the null will fly.” Given that a hypothesis test never results in a conclusion of proving or supporting a null hypothesis, how is this memory trick misleading? Exercise Sample Proportion In a Wakefield Research survey, respondents were asked if they ever hesitated to give a handshake because of a fear of germs. Of the respondents, 411 answered “yes” and 592 said “no.” What is the sample proportion of yes responses, and what notation is used to represent it?

Problem 5BSC identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Assume a 0.05 significance level and answer the following: a.Is the test two-tailed, left-tailed, or right-tailed? b.What is the test statistic? c.What is the P-value? d.What is the null hypothesis, and what do you conclude about it? e.What is the final conclusion? Adverse Reactions to DrugThe drug Symbicort is used to treat asthma. In a clinical trial of Symbicort, 18 of 277 treated subjects experienced headaches (based on data from AstraZeneca). The accompanying TI-83/84 Plus calculator display shows results from a test of the claim that less than 10% of treated subjects experienced headaches.

In Exercises 5–8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Assume a 0.05 significance level and answer the following: a. Is the test two-­tailed, left-­tailed, or right-­tailed? b. What is the test statistic? c. What is the P-­value? d. What is the null hypothesis, and what do you conclude about it? e. What is the final conclusion? Guns in the Home In a Gallup poll of 1003 randomly selected subjects, 373 said that they have a gun in their home. The accompanying Minitab display shows results from a test of the claim that 35% of homes have guns in them. MINITAB

In Exercises 5–8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Assume a 0.05 significance level and answer the following: a. Is the test two-­tailed, left-­tailed, or right-­tailed? b. What is the test statistic? c. What is the P-­value? d. What is the null hypothesis, and what do you conclude about it? e. What is the final conclusion? Brand Recognition A PriceGrabber.com survey of 1631 randomly selected adults showed that 555 of them have heard of the Sony Reader. The following STATDISK display results from a test of the claim that 35% of adults have heard of the Sony Reader. STATDISK

In Exercises 5–8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Assume a 0.05 significance level and answer the following: a. Is the test two-­tailed, left-­tailed, or right-­tailed? b. What is the test statistic? c. What is the P-­value? d. What is the null hypothesis, and what do you conclude about it? e. What is the final conclusion? Public Speaking A TNS poll of 1000 randomly selected adults showed that 460 of them say that public speaking is an activity that they dread most. Shown next is the StatCrunch display resulting from a test of the claim that fewer than half of adults say that public speaking is the activity that they dread most. STATCRUNCH

Problem 9BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unhas your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Use a 0.01 significance level to test Mendel’s claim that under the same circumstances, 25% of offspring peas will be yellow.

Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-­value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). M&Ms Data Set 20 in Appendix B lists data from 100 M&Ms, and 8% of them are brown. Use a 0.05 significance level to test the claim of the Mars candy company that the percentage of brown M&Ms is equal to 13%.

Problem 11BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unhas your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Identify Theft In a KRC Research poll, 1002 adults were asked if they felt vulnerable to identity theft, and 531 of them said “yes.” Use a 0.05 significance level to test the claim that the majority of adults feel vulnerable to identity theft.

Problem 12BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unhas your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Plane Seats In a 3M Privacy Filters poll, 806 adults were asked to identify their favorite seat when they fly, and 492 of them chose a window seat. Use a 0.01 significance level to test the claim that the majority of adults prefer window seats when they fly.

Problem 13BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unhas your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Gender Selection The Genetics & IVF Institute conducted a clinical trial of the XSORT method designed to increase the probability of conceiving a girl. As of this writing, 945 babies were born to parents using the XSORT method, and 879 of them were girls. Use a 0.01 significance level to test the claim that the XSORT method is effective in increasing the likelihood that a baby will be a girl.

Problem 14BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unhas your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Gender Selection The Genetics & IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability of conceiving a boy. As of this writing, 291 babies were born to parents using the YSORT method, and 239 of them were boys. Use a 0.01 significance level to test the claim that the YSORT method is effective in increasing the likelihood that a baby will be a boy.

Problem 15BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Touch Therapy When she was 9 years of age, Emily Rosa did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, then she asked the therapists to identify the selected hand by placing their hand just under Emily’s hand without seeing it and without touching it. Among 280 trials, the touch therapists were correct 123 times (based on data in “A Close Look at Therapeutic Touch, ” Journal of the American Medical Association, Vol. 279, No. 13). Use a 0.10 significance level to test the claim that touch therapists use a method equivalent to random guesses. Do the results suggest that touch therapists are effective?

Problem 16BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Touch Therapy Repeat the preceding exercise using a 0.01 significance level. Does the conclusion change?

Problem 17BSC test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Tennis Instant Replay The Hawk-Eye electronic system is used in tennis for displaying an instant replay that shows whether a ball is in bounds or out of bounds so players can challenge calls made by referees. In the most recent U.S. Open (as of this writing), singles players made 611 challenges and 172 of them were successful with the call overturned. Use a 0.01 significance level to test the claim that fewer than 1/3 of the challenges are successful. What do the results suggest about the ability of players to see calls better than referees?

Problem 18BSC test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Perception and Reality In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won (based on data from ICR Survey Research Group). Use a 0.10 significance level to test the claim that among all voters, the percentage who believe that they voted for the winning candidate is equal to 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions?

Problem 19BSC test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Cell Phones and Cancer In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported inUSA Today).Test the claim of a somewhat common belief that such cancers are affected by cell phone use. That is, test the claim that cell phone users develop cancer of the brain or nervous system at a rate that is different from the rate of 0.0340% for people who do not use cell phones. Because this issue has such great importance, use a 0.005 significance level. Based on these results, should cell phone users be concerned about cancer of the brain or nervous system?

Problem 20BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Twitter Poll The Pew Research Center conducted a survey of 1007 adults and found that 856 of them know what Twitter is. Use a 0.01 significance level to test the claim that more than 75% of adults know what Twitter is.

Problem 21BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Overtime Rule in Football In “The Overtime Rule in the National Football League: Fair or Unfair?” by Gorgievski et al., Mathamatyc Educator, Vol. 2, No. 1, the authors report that among 414 football games won in overtime, 235 were won by the team that won the coin toss at the beginning of overtime. Using a 0.05 significance level, test the claim that the coin toss is fair in the sense that neither team has an advantage by winning it.

Problem 22BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Testing Effectiveness of Nicotine Patches In one study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after the treatment and 32 were not smoking one year after the treatment (based on data from “High-Dose Nicotine Patch Therapy, ” by Dale et al., Journal of the American Medical Association, Vol. 274, No. 17). Use a 0.05 significance level to test the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment. What do these results suggest about the effectiveness of nicotine patch therapy for those trying to quit smoking?

Problem 23BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Smartphone Users A RingCentral survey of 380 smartphone users showed that 152 of them said that their smartphone is the only thing they could not live without. Use a 0.01 significance level to test the claim that fewer than half of smartphone users identify the smartphone as the only thing they could not live without. Do these results apply to the general population?

Problem 24BSC test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Postponing Death An interesting and popular hypothesis is that individuals can temporarily postpone death to survive a major holiday or important event such as a birthday. In a study of this phenomenon, it was found that there were 6062 deaths in the week before Thanksgiving, and 5938 deaths the week after Thanksgiving (based on data from “Holidays, Birthdays, and Postponement of Cancer Death,” by Young and Hadz, Journal of the American Medical Association,Vol. 292, No. 24). If people can postpone death until after Thanksgiving, then the proportion of deaths in the week before should be less than 0.5. Use a 0.05 significance level to test the claim that the proportion of deaths in the week before Thanksgiving is less than 0.5. Based on the result, does there appear to be any indication that people can temporarily postpone death to survive the Thanksgiving holiday?

Problem 25BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Online Books A Consumer Reports Research Center survey of 427 women showed that 29.0% of them purchase books online. Test the claim that more than 25% of women purchase books online.

Problem 26BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Job Interviews In a Harris poll of 514 human resource professionals, 45.9% said that body piercings and tattoos were big grooming red flags. Use a 0.01 significance level to test the claim that less than half of all human resource professionals say that body piercings are big grooming red flags.

Problem 27BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Job Interviews In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job applicant is most important for a good first impression. Use a 0.01 significance level to test the claim that more than 3/4 of all human resource professionals say that the appearance of a job applicant is most important for a good first impression.

Problem 28BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Misleading Survey Responses Voting records show that 61% of eligible voters actually did vote in a recent presidential election. In a survey of 1002 people, 70% said that they voted in that election (based on data from ICR Research Group). Use the survey results to test the claim that the percentage of all voters who say that they voted is equal to 61%. What do the results suggest?

Problem 29BSC test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Bias in Jury Selection In the case of Casteneda v. Partida,it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry. Use a 0.01 significance level to test the claim that the selection process is biased against Americans of Mexican ancestry. Does the jury selection system appear to be fair?

Problem 30BSC test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Finding a Job Through Networking In a survey of 703 randomly selected workers, 61% got their jobs through networking (based on data from Taylor Nelson Sofres Research). Use the sample data with a 0.05 significance level to test the claim that most (more than 50%) workers get their jobs through networking. What does the result suggest about the strategy for finding a job after graduation?

Problem 31BSC test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). Nielsen Ratings A recent Super Bowl football game between theNew Orleans Saints and the Indianapolis Colts set a record for the number of television viewers. According to the Nielsen company, that game had a share of 77%, meaning that among the television sets in use at the time of the game, 77% were tuned to the game. Nielsen’s sample size is 25,000 households. Use a 0.01 significance level to test the claim of a media report that more than 75% of television sets in use were tuned to the Super Bowl.

Problem 32BSC Testing Claims about Proportions. In Exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section). HDTV Penetration In a survey of 1500 households, it is found that 47% of them have a high-definition television (based on data from the Consumer Electronics Association). Use a 0.01 significance level to test the claim that fewer than half of all households have a high-definition television. Is the result from a few years ago likely to be valid today?

Large Data Sets. In Exercises 33 and 34, use the data set from Appendix B to test the given claim. M&Ms Refer to Data Set 20 in Appendix B and find the sample proportion of M&Ms that are green. Use that result to test the claim of Mars, Inc., that 16% of its plain M&M candies are green.

Large Data Sets. In Exercises 33 and 34, use the data set from Appendix B to test the given claim. On-­Time Flights Consider a flight to be on time if it arrives no later than 15 minutes after the scheduled arrival time. Refer to Data Set 15 in Appendix B, and use the sample data to test the claim made by CNN that 79.5% of flights are on time. Use a 0.05 significance level.

Problem 35BB Binomial Distribution We want to use a 0.05 significance level to test the claim that a coin favors heads, and sample data consist of 7 heads in 8 tosses. We can’t use the normal approximation method because we violate the requirement that np ? 5 and nq ? 5. Use the binomial probability distribution to test the claim.

Problem 36BB Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1. a. Use the critical value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1. ________________ b. Use the P-value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1. ________________ c. Use the sample data to construct a 95% confidence interval estimate of the proportion of zeros. What does the confidence interval suggest about the claim that the proportion of zeros equals 0.1? ________________ d. Compare the results from the critical value method, the P-value method, and the confidence interval method. Do they all lead to the same conclusion?

Problem 37BB Power For a hypothesis test with a specified significance level ?, the probability of a type I error is a, whereas the probability ? of a type II error depends on the particular value of p that is used as an alternative to the null hypothesis. a. Using an alternative hypothesis of p < 0.4, a sample size of n = 50, and assuming that the true value of p is 0.25, find the power of the test. See Exercise 1 in Section 8-2. (Hint: Use the values p= 0.25 and pq/n = (0.25)(0.75)/50.) ________________ b. Find the value of ß, the probability of making a type II error. ________________ c. Given the conditions cited in part (a), what do the results indicate about the effectiveness of the hypothesis test? Exercise 1 Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.