Concept explainers
The article “U.S. Investors Split Between Digital and Traditional Banking” (gallup.com, August 5, 2016, retrieved April 25, 2017) summarized data from a Gallup survey of a random sample of 1019 U.S. adults with investments of $10,000 or more. Based on the survey data, it was estimated that 31 % of investors manage their investments by doing everything they possibly can online. But the authors of the article also noted that there was quite a difference between younger investors (age 18 to 49) and older investors (age 50 and older). For younger investors, 43% said they do everything they possibly can online, while the percentage for older investors was 23%.
- a. Use the given information to estimate P(O), P(O|Y), and P(O|F) where O =
event that a randomly selected investor does everything possible online, Y = event that a randomly selected investor is age 18 to 49, and F = event that a ran do ml y selected investor is 50 years old or older. - b. Suppose that 40% of investors are between the ages of 18 and 49. Use the probabilities from Part (a) and the estimate P(Y) = 0.40 to calculate P(Y|O) and write a sentence interpreting this value.
6.81 The accompanying table summarizes data from a medical expenditures survey carried out by the National Center for Health Statistics (“Assessing the Effects of Race and Ethnicity on Use of Complementary and Alternative Therapies in the USA,” Ethnicity and Health [2005]: 19-32).
These percentages were based on data from 7320 people whose education level was high school or less, 4793 people with I to 4 years of college, and 1095 people with 5 or more years of college.
- a. Use the information given to determine the number of respondents falling into each of the six cells of the table below.
- b. Construct a table of estimated probabilities by dividing the count in each of the six table cells by the total sample size, n = 13,208.
- c. The authors of the study indicated that the sample was selected in a way that makes it reasonable to regard the estimated probabilities in the table from Part (b) as representative of the adult population in the United States. Use the information in that table to estimate the following probabilities for adults in the United States.
- i. The
probability that a randomly selected individual has 5 or more years of college. - ii. The probability that a randomly selected individual uses alternative therapies.
- i. The
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Introduction To Statistics And Data Analysis
- "Streaming" of television programs is trending upward. According to The Harris Poll (August 26, 2013), over one- third of American's qualify as "subscription streamers," i.e., those who watch streamed TV programs through a subscription service such as Netflix, Hulu Plus, or Amazon Prime. The poll included 2,242 adult TV viewers, of which 785 are subscription streamers. On the basis of this result, can you conclude that the true fraction of adult TV viewers who are subscription streamers differs from one-third? Carry out the test using a Type I error rate of a a = 0.10. Be sure to give the null and alternative hypotheses tested, test statistic value, rejection region or p-value, and conclusion. Problem 26 andarrow_forwardAccording to a Gallup survey two years ago, 32% of American households use a computer or online financial program to manage their money. Suppose analysts believe that this figure has increased recently, and they test their theory by randomly sampling 85 American households. Of the 85 households, 36% respond that they do use a computer or online financial program to manage their money. Is this result enough evidence to conclude that a significantly higher proportion of American households use a computer or online financial program to manage their money? Let a = .10. Appendix A Statistical Tables (Round your answer to 2 decimal places, e.g. 15.25.) The value of the test statistic is and wearrow_forward6) Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.A sample of 62 stocks traded on the NYSE that day showed that 24 went up.You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of α=0.001α=0.001.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... PICK ONE less than (or equal to) αα greater than αα This test statistic leads to a decision to... PICK ONE reject the…arrow_forward
- Mr. William Profit is studying companies going public for the first time. He is particularlyinterested in the relationship between the size of the offering and the price per share.A sample of 15 companies that recently went public revealed the following information.arrow_forwardA friend of yours tells you that they heard that 65% of all college athletes end up losing a finger or toe in their college athletic career. You're highly skeptical of this, but your not sure if that percentage is an over exageration or an under exageration. You survey 101 former student-athletes and find that 60 of them lost a digit during their college athletic career. Is this enough evidence to conclude that the true percentage of student-athletes that lose a digit during their collegiate career is really different from 65%?arrow_forwardA Bloomberg Businessweek North American subscriber study collected data from asample of 2861 subscribers. Fifty-nine percent of the respondents indicated an annualincome of $75,000 or more, and 50% reported having an American Express credit card.a. What is the population of interest in this study?b. Is annual income a categorical or quantitative variable?arrow_forward
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- According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, assume some state had 454 complaints of identity theft out of 1660 consumer complaints. Do these data provide enough evidence to show that the state had a higher proportion of identity theft than 23%? Test at the 10% level.arrow_forwardExplain the Holt-Winter and Brown forecasting techniquearrow_forward“The US Centers for Disease Control and Prevention said about 72 million Americans—nearly one out of every four of the country’s 304 million residents—are considered obese. Millions more are designated as overweight.” The American trend toward obesity has prompted many physicians to offer weight-loss programs to their patients. [Source: Price, W. T. “Physicians Get into the Weight-Loss Business.” Florida Today, July 7, 2008.] A physician conducted an experimental study to compare the effectiveness of four different weight-loss programs. In the study, 64 obese adults were randomly assigned to the four programs so that each program had 16 adults. The programs lasted for six months. The weights of the subjects were measured before and after the programs, and each subject’s weight loss was computed in pounds. The following table summarizes the results of the study, giving the number of observations and the sample mean and variance of the subjects’ weight loss in each program.…arrow_forward
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