9. A study of the post treatment behavior of a large number of drug abusers suggests that the likelihood of conviction within a two-year period after treatment may depend upon the offenders' education. the study is conducted on 750 people. The number of cases falling in four education-conviction categories are shown in the following table: Status within 2 years after treatment Education Convicted Not Convicted Total 75 325 10 years or more 9 years or less Total 250 125 300 425 200 550 750 Suppose that a single offender is selected from the treatment program. Define the events; A: The offender has 9 or less years of education. B: The offender is convicted within two years after completion of treatment. Find the following: a. P(A) b. P(B) c. P(AN B) d. P(A U B) e. P(An B) f. P(AU B)
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- Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain asked this question. Some data collected by the chain are summarized in the table below. The data were obtained from a random sample of 180 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of the table are the frequencies observed in the sample for these season categories. The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The bottom row of numbers gives the following value for each of the season categories. (Each expert I have asked has gotten the critical value wrong so I added a picture of the correct formula to…Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain asked this question. Some data collected by the chain are summarized in the table below. The data were obtained from a random sample of 180 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of the table are the frequencies observed in the sample for these season categories. The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The bottom row of numbers gives the following value for each of the season categories. (Each expert I have asked has gotten the critical value wrong so I added a picture of the correct formula to…4. Straight As now, healthy later A study by Pamela Herd of the University of Wisconsin-Madison found a link between high-school grades and health. Analyzing data from the Wisconsin Longitudinal Study, which has tracked the lives of thousands of Wisconsin high-school graduates from the class of 1957, Herd found that students with higher grade-point averages were more likely to say they were in excellent or very good health in their early 60s. Does this mean people will live healthier lives if they increase their GPA? Explain.47
- A survey described the results of a poll of working adults in Canada. Each person in a random sample was classified according to gender and the number of vacation days he or she usually took each year. The resulting data are summarized in the given table. Days of Vacation Gender Male Female None 51 42 1-5 21 25 6-10 67 79 11-15 106 98 16-20 71 70 21-25 82 58 More than 25 118 79 (a) Is it reasonable to conclude that there is an association between gender and the number of vacation days taken?Test the appropriate hypotheses using a 0.05 significance level. Calculate the test statistic. (Round your answer to two decimal places.)?2 =The table below shows the auto insurance quotes for two leading companies for a sample of 15 families. Assume the populations SDs are similar, but unknown. The President of the American Insurance Institute wants to compare the yearly costs of such insurance offered by the two companies. At the 0.10 level of significance, can we conclude that there is a difference in the amounts quoted? Families Southern Car American Mutual ($) ($) 1 2090 1610 2 1683 1247 3 1402 2327 4 1830 1367 5 930 1461 6 697 1789 7 1741 1621 8 1129 1914 9 1018 1956 10 1881 1772 11 1571 1375 12 874 1527 13 1579 1767 14 1577 1636 15 860 1188A study prospectively examined whether sleep-disordered breathing was associated with an increased risk of death from any cause in a cohort of 600 adults participating in the Sleep Heart Health Study. Study participants were classified into four groups depending on the extent of their sleep-disordered breathing (none, mild, moderate, or severe). The counts of deaths over the course of the study are reported for each group in the following two-way table. Mild Severe 100 Death No Death Total None 40 100 140 40 100 140 Moderate 20 100 120 Total 200 400 600 100 200 We want to know whether the study findings give evidence of a significant difference of the number of deaths between the different groups. Set up the alternative hypothesis (H, : The distribution of the categorical variable is not as given by the null hypothesis (lack of fit) At least ones of the means is different from the others O The two categorical variables are dependent The distribution of the categorical variable is not…
- A study prospectively examined whether sleep-disordered breathing was associated with an increased risk of death from any cause in a cohort of 600 adults participating in the Sleep Heart Health Study. Study participants were classified into four groups depending on the extent of their sleep-disordered breathing (none, mild, moderate, or severe). The counts of deaths over the course of the study are reported for each group in the following two-way table. Death No Death Total None 40 100 140 Mild 40 100 140 Moderate 20 100 120 Severe 100 100 200 Total 200 400 600 We want to know whether the study findings give evidence of a significant difference of the number of deaths between the different groups. The observed test statistic is 3.610 42.857 5.476 8.075A random survey of health issues, conducted by the Department of Public Health of the Commonwealth of Massachusetts, examined the results from the state's seven largest cities. These cities were selected on the basis of their diverse racial and ethnic populations. The percentage of adults with diabetes in each city in the survey is given in the following table. City Boston Worcester Springfield Lowell Fall River Lawrence NewBedford Adults withDiabetes (%) 4.2 5.2 9.1 5.7 8.1 7.9 6.3 Find the average percentage of adults with diabetes in these seven cities. (Round your answer to two decimal places.) %What is the standard deviation for these data? (Round your answer to two decimal places.) %Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data: B: Percent for company 5 8 13 16 14 20 4 13 A: Percent for CEO 2 –1 3 14 19 17 3 9 Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 1% level of significance. Are the data statistically significant at level α? Will you reject or fail to reject the null hypothesis? choose one: a) Since the interval containing the P-values has values that are smaller than the level of significance, the data are statistically significant and so we reject the null hypothesis. b) Since the interval containing…
- A cross-sectional study is conducted to investigate cardiovascular disease (CVD) risk factors among a sample of patients seeking medical care at one of three local hospitals. A total of 500500 patients are enrolled. Based on the following data, we would like to determine if there is a significant association between the family history of CVD and the enrollment site. Enrollment Site Family History of CVD Hospital 1 Hospital 2 Hospital 3 Total Yes 34 8 58 100 No 104 72 224 400 Total 138 80 282 500 Given: The value of the test statistic is χ2= 6.912 Use α=0.1 as the level of significance. The superintendent of Hospital 2 performed the Goodness of Fit Test to test whether 25% of the patients go to Hospital 1, 15% of the patients go to Hospital 2 and 60% of the patients go to Hospital 3. Given: The superintendent found that the pp-value for the test is 0.25091 Let: p1=p1= be the proportion of patients at Hospital 1 p2=p2= be the proportion of patients at…1. A developmental psychologist would also like to determine how much fine motor skill improves for children from age 3 to age 4 but is worried about practice effects. She takes a random sample of 9 three-year old children and a second sample of 9 four-year olds and measures fine motor skill in each using the same test described above. Her data are provided below. Three Year Olds: 40, 35, 38, 39, 40, 50, 40, 38, 42 Four Year Olds: 35, 36, 39, 29, 35, 34, 33, 34, 35 a. Is there a significant difference in the motor skills from age three to four? Test with an α = 0.01. b. What type of error is possible based on the outcome? c. Calculate and interpret the effect size. d. What is the mean motor skill score for the age three children? What is the mean motor skill score for the age four children?