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MATH 2565 (19)
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PPS8_Solution_.doc

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Department
Mathematics and Statistics
Course
MATH 2565
Professor
Jagmohan Chawla
Semester
Winter

Description
PPS8(Solution) Problem 23.3 t-models, part III. As the number of degrees of freedom increases, the centres of t-models do not change. The spread of t-models decreases as the number of degrees of freedom increases, and the shape of the distribution becomes closer to Normal. Problem 23.7 Meal plan. a)Not correct. The confidence interval is not about the individual students in the population. b) Not correct. The confidence interval is not about individual students in the sample. In fact, we know exactly what these students spent, so there is no need to estimate. c)Not correct. We know that the mean cost for students in this sample was $1196. d) Not correct. A confidence interval is not about other sample means. e) This is the correct interpretation of a confidence interval. It estimates a population parameter. Problem 23.9 Pulse rates. a)We are 95% confident the interval 70.9 to 74.5 beats per minute contains the true mean heart rate. b) The width of the interval is about 74.5 – 70.9 = 3.6 beats per minute. The margin of error is half of that, about 1.8 beats per minute. c)The margin of error would have been larger. More confidence requires a larger critical value of t, which increases the margin of error. Problem 23.15. Normal temperatures, part II. a)The 90% confidence interval would be narrower than the 98% confidence interval. We can be more precise with our interval when we are less confident. b) The 98% confidence interval has a greater chance of containing the true mean body temperature of adults than the 90% confidence interval, but the 98% confidence interval is less precise (wider) than the 90% confidence interval. c)The 98% confidence interval would be narrower if the sample size were increased from 52 people to 500 people. The smaller standard error would result in a smaller margin of error. d) Our sample of 52 people gave us a 98% confidence interval with a margin of error of (36.96 – 36.7)/2 =0.13°C. In order to get a margin of error of 0.05, less than half of that, we need a sample over 4 times as large. It should be safe to use t
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