MATH PROJECT 2 MR GURURU

Mini-Project #2 Math 243, Summer ’19

Complete each portion of the mini-project as indicated on the next pages. Your submitted project should be clean and legible. It will be graded for accuracy, readability, and work shown.

This mini-project is due in class on Aug 14.

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Mini-Project #2 Math 243, Summer ’19

Part 1 - Postponement theory: Larsen and Marx write1

There is a theory that people may tend to “postpone” their deaths until after some event that has particular meaning to them has passed. Birthdays, a family reunion, or the return of a loved one have all been suggested as the sorts of personal milestones that might have such an effect. In a study to set up to examine that notion statistically, it was found that only 60 of 747 people whose obituaries were published in Salt Lake City in 1975 died in the three-month period preceding their birthday.

1. Construct a 90% confidence interval for the true proportion of people who die in the three-month period preceding their birthday.

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2. Write a sentence explaining what the “90%” part of the confidence interval from the previous problem means. The sentence should not refer to probability nor chance.

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1Larsen, R. J., and Marx, M. L. (1986). An Introduction to Mathematical Statistics and Its Applications. Second Edition. Prentice- Hall, Englewood Cliffs, New Jersey, page 295.

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Mini-Project #2 Math 243, Summer ’19

3. How large of a sample would we need, at a 90% confidence level, to estimate the true proportion of people who died in the three-month period preceding their birthday with a margin of error no greater than 0.001?

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4. If individuals are dying randomly with respect to their birthday, we would expect 25% to die during the three-month period preceding their birthday. Based on the confidence interval you constructed in Problem 1, and at a 5% significance level, do we have convincing evidence that the true proportion of deaths that occur in the three month period before a decedents’s birthday is less than 25%? Why?

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Mini-Project #2 Math 243, Summer ’19

Part 2 - Cloud Seeding: Cloud seeding is a form of weather modification that attempts to change the amount or type of rain that falls from clouds. In one experiment2, 52 clouds were selected, and 26 of them were chosen at random and seeded with silver nitrate. Their results are shown below.

Sample mean (acre-ft) Sample standard deviation (acre-ft) Sample size

Unseeded clouds x1 = 164.59 s1 = 278.42 n1 = 26

Seeded clouds x2 = 441.98 s2 = 650.79 n2 = 26

5. In this experiment, what is the sample, the population, explanatory variable(s) and response variables?

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6. There appears to be a difference in the mean rainfall between the unseeded and seeded clouds. Is there sufficient evidence, at the 5% significance level, to support the claim that the mean rainfall of seeded clouds is higher than that of unseeded clouds?

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2Simpson, Alsen, and Eden. (1975). A Bayesian analysis of a multiplicative treatment effect in weather modification. Technometrics 17, 161-166.

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Mini-Project #2 Math 243, Summer ’19

Below, we have included the histograms of the rainfall for both the unseeded and seeded clouds (note that the horizontal scales are not the same).

Seeded clouds Unseeded clouds

7. Briefly describe why our data does not meet the strict guidelines necessary to perform a two-sample t-test.

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8. Are we able to trust the conclusion from Problem 6, even though the data does not meet the strict guidelines for performing a two-sample t-test? Explain.

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Presentation:

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Total:

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