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Answers to 2Sample Confidence Intervals 1 Mean annual profit as % of revenue for insurance company 1. 2 Mean annual profit as % of revenue for health care company Difference in mean annual profit as % between insurance and health care companies 2 1 Assumptions: 1. Independent random samples 2. App. normal (Boxplots sym) n1 & n2< 30 x x t 1 2 s12 s22 n1 n2 1.304, 0.90364 Use 2 sample T-Interval We’re 90% confident that the mean difference in mean annual profit as % in insurance & health care companies is between -1.304 and 0.90364. Since the interval contains 0, there is no significant difference between them. 1 Mean height of professional football players 2. 2 Mean height of professional basketball players Difference in mean height of professional football and basketball players 2 1 Assumptions: 1. Independent random samples 2. Approximately normal since n1 & n2>30 x1 x 2 z s12 s22 n1 n2 0.4146, 0.1254 Use 2 sample Z-Interval 3. Mean yearly salary H o : 29800 H A : 29800 Assumptions: 1. Simple random samples 2. Approximately normal Since n > 30 We’re 95% confident that the mean height of professional football players is between 0.4146 and 0.1254 feet shorter than professional basketball players. Use 1 sample Z-Test x 8 s n p value ncdf (8, ) 0 z Reject the Ho since p-value <α. There’s sufficient evidence to support the claim that the mean yearly salary is less than $29,800. 1 Mean percentage of salary increase for professors at eastern colleges 4. 2 Mean percentage of salary increase for professors at western colleges Difference in mean % of salary increases between eastern & western colleges 2 1 Assumptions: 1. Independent random samples 2. Approximately normal since n1 & n2>30 Use 2 sample Z-Interval x1 x 2 z s12 s22 n1 n2 0.3319, 0.93193 We’re 90% confident that the mean % of salary increase in professor salaries between eastern & western colleges is between -0.3319 and 0.93193. Since the interval contains 0, there’s no significant difference. 1 Mean weight of male wolves from Canadian Northwest Territories 5. 2 Mean weight of male wolves from Alaska Difference in mean weight of males wolves from Canada & Alaska 2 1 Assumptions: 1. Independent random samples 2. App normal (Box plots sym) since n1 & n2<30 x x t 1 s12 s22 n1 n2 2 6.52 7.32 18 24 98 90 2.110 3.5, 12.5 Use 2 sample T-Interval We’re 95% confident that the mean weight of male wolves from Canada are between 3.5 and 12.5 pound heavier than the male wolves from Alaska. 1 Mean number of children in low income families 6. 2 Mean number of children in high income families Difference in mean number of children between low and high income families 2 1 Assumptions: 1. Independent random samples 2. App normal (Boxplot sym) since n1 & n2<30 s2 s2 x1 x 2 t 1 2 n1 n2 1.314, 2.6537 Use 2 sample T-Interval We’re 95% confident that the mean difference in the number of children between low income families and high income families is between 1.314 and 2.6537. Since the interval contains 0, there’s no significant difference. 1 Mean score on reading test in the control group 7. 2 Mean score on reading test in the experimental group Difference in mean reading scores between control and experimental groups 2 1 H o : 1 2 0 H A : 1 2 0 Assumptions: 1. Independent random samples 2. Approximately normal since n1 & n2>30 Use 2 sample Z-Test z x x 1.552 1 2 1 2 1 2 2 2 Fail to Reject Ho since p-val >α Insufficient evidence to support the claim that the experimental group scored higher. s s n1 n2 p value 0.0637 8. mean number of days spent in the hospital Assumptions: 1. Simple random samples 2. App normal (boxplot sym) since n>30 Use 1 sample T-Interval s xt n 6.6753, 7.898 We’re 99% confident that the mean number of days patients spend in the hospital is between 6.6753 and 7.898 days.