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- A research paper describes a study of the relationship between age and 1-hour swimming performance. Data on age and swim distance for over 10,000 men participating in a national long-distance 1-hour swimming competition are summarized in the accompanying table. Representative Age (Midpoint of Age Group) Average Swim Distance (meters) Age Group 20-29 25 3913.5 30-39 35 3718.8 40-49 45 3579.4 50-59 55 3351.9 60-69 65 3000.1 70-79 75 2639.0 80-89 85 2118.4 (a) Find the equation of the least-squares line with x = representative age and y = average swim distance. (Round your numerical values to three decimal places.) + (b) Compute the seven residuals. (Round your answers to three decimal places.) Representative Age (x) Residual (meters) 25 35 45 55 65 75 85 Use the seven residuals to construct a residual plot. Residual Residual Residual 200 200 200 100 100 100 - 100 -100 - 100Winning team data were collected for teams in different sports, with the results given in the table below. Use the TI-83/84 Plus results at a 0.05 level of significance to test the claim that home/visitor wins are independent of the sport. TI-83/84 PLUS χ2−Test χ2=12.088928047 P=0.0070846566 df=3 Basketball Baseball Hockey Football Home team wins 142 59 49 41 Visiting team wins 65 42 36 45 Reject Fail to reject the null hypothesis that home/visitor wins are independent of the sport. It appears that the home-field advantage ▼ does does not depend on the sport.ANOVA. Dr. Milgramm is conducting a patient satisfaction survey, rating how well her patients like her on a scale of 1-10. Her patients tend to fall into three categories: “Like a lot”, “like somewhat”, and “dislike a lot”. She believes that she might get different satisfaction scores from people in each group, but (because she's not great at numbers) she wants you to do an ANOVA to be sure. She has collected data from 12 patients (three equal groups) with the following results. Group 1) “Like a lot” Mean: 8 SS: 2 N: df: Group 2) “Like somewhat” Mean: 5 SS: 6 N: df: Group 3) “Dislike a lot” Mean: 2 SS: 4 N: df: Grand Mean: df Within-Group:__________ df Between-Groups:___________ Estimated Variance (S21) for Group 1: _______ Estimated Variance (S22) for Group 2: ___________ Estimated…
- A researcher wants to investigate whether single people who own pets are happier than singles without pets. A mood inventory is administered to a group of 20-29 years old non-pet owners and a similar age group of pet owners. The pet owners are also matched one one one with non-pet owners for income, number of close friends, and general health. The data are as follows: Non-pet owner pet owner 10 15 9 9 11 10 11 19 5 17 9 15 is there a significant difference in the mood scores for non-pet owners and pet owners?Practice question #3 Investigators want to know if those who work long hours have more trouble sleeping. In one sample of 190 British civil servants who worked more than 40 hours a week, 95 of them said they usually get less than 7 hours of sleep per night. In a second sample of 150 British civil servants who worked between 35 and 40 hours per week, 63 of them said they usually get less than 7 hours of sleep per night. The investigators believe these are represent samples of the populations. Find a 95% Confidence Interval for the difference in proportions of these two populations that get less than 7 hours of sleep per night. Then interpret the confidence interval. Be sure to check that any necessary conditions are met first. Round final answers to 3 decimal places. Verify conditions are appropriate for method: Interval: ________________________ Does the interval contain zero? __________ What does this information lead you to conclude?Government economic studies reveal that young adults, not middle-aged or older adults, are having the most difficult time in today’s economy. Although the nation’s labor market shows a decline in the unemployment rate, the percentage of young adults, ages 18 to 24, currently employed (54 percent) is at the lowest level since the government data collection began in 1948. If you were working for a national survey organization doing a general public survey of young adults and older adults, what topics and questions would you design into your survey to elaborate on this finding?
- Is there a relation between incidents of child abuse and number of runaway children? A random sample of cities (over 10,000 population) gave the following information about the number of reported incidents of child abuse and the number of runaway children. (Reference: Federal Bureau of Investigation, U.S. Department of Justice.) City 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Abuse cases 113 33 41 60 52 99 31 56 15 67 106 59 45 74 84 Runaways 648 188 285 687 421 590 284 277 162 473 600 432 317 580 592 Use a 1% level of significance to test the claim that there is a monotone-increasing relationship between the ranks of incidents of abuse and number of runaway children. (a) Rank-order abuse using 1 as the largest data value. Also rank-order runaways using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test. City Abuse CasesRank x RunawaysRank y d = x - y d2 123456789101112131415 Σd2 = (b) What is the level of…A researcher wants to study the relationship between salary and gender. She randomly selects 392 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent? Income Male Female Total Below $25,000$25,000 48 45 93 $25,000$25,000-$50,000$50,000 38 36 74 $50,000$50,000-$75,000$75,000 46 40 86 Above $75,000$75,000 68 71 139 Total 200 192 392 State the conclusion of the hypothesis test at the 0.010.01 level of significance.A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 250250 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 250250 individuals and asks them the same questions. Can the psychologist confirm his theory that the attitudes have changed from the first survey to the second survey? Attitude 1st Survey 2nd Survey Optimistic 50%50% 52%52% Slightly Optimistic 16%16% 10%10% Slightly Pessimistic 11%11% 15%15% Pessimistic 23%23% 23%23% Copy Data Step 6 of 10 : Find the value of the test statistic. Round your answer to three decimal places. Step 7 of 10: Find the degrees of freedom associated with the test statistic for this problem Step 8 of 10: Find the critical value of the test at the 0.025 level of significance. Round your answer to three decimal places.step 9 of 10: make the decision to reject or fail to reject…