Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50-Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight-year period. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) In words, define the random variables X and P' ○ X is the proportion of people who ran and died in the eight-year period, and P' is the number of people who ran and died in the eight-year period. ○ X is the proportion of all runners that die, and P' is the number of all runners that die. ○ X is the number of people who ran and died in the eight-year period, and P'is the proportion of people who ran and died in the eight-year period. OX is the number of all runners that die, and P'is the proportion of all runners that die. Part (b) Which distribution should you use for this problem? (Round your answers to four decimal places.) P'~ Explain your choice. The Student's t-distribution should be used because √npq ≤ 10, which implies a small sample. The standard normal distribution should be used because we are interested in proportions. O The binomial distribution should be used because the two outcomes are "the runner died" and "the runner did not die." ○ The Student's t-distribution should be used because we do not know the standard deviation. Part (c) Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period. (i) State the confidence interval. (Round your answers to four decimal places.) (ii) Sketch the graph. α C.L.= (iii) Calculate the error bound. (Round your answer to four decimal places.) 82 P' Part (d) Explain what a "97% confidence interval" means for this study. There is a 97% chance that a runner over the age of 50 will die. We are 97% confident that fewer than 3% of people over the age of 50 are runners. ○ We are 97% confident that the population proportion of runners over the age of 50 that will die in the next eight years is between the interval values. ○ We are 97% confident that the number of deaths of runners over the age of 50 is less than 3 people.

Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50-Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight-year period. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) In words, define the random variables X and P' ○ X is the proportion of people who ran and died in the eight-year period, and P' is the number of people who ran and died in the eight-year period. ○ X is the proportion of all runners that die, and P' is the number of all runners that die. ○ X is the number of people who ran and died in the eight-year period, and P'is the proportion of people who ran and died in the eight-year period. OX is the number of all runners that die, and P'is the proportion of all runners that die. Part (b) Which distribution should you use for this problem? (Round your answers to four decimal places.) P'~ Explain your choice. The Student's t-distribution should be used because √npq ≤ 10, which implies a small sample. The standard normal distribution should be used because we are interested in proportions. O The binomial distribution should be used because the two outcomes are "the runner died" and "the runner did not die." ○ The Student's t-distribution should be used because we do not know the standard deviation. Part (c) Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period. (i) State the confidence interval. (Round your answers to four decimal places.) (ii) Sketch the graph. α C.L.= (iii) Calculate the error bound. (Round your answer to four decimal places.) 82 P' Part (d) Explain what a "97% confidence interval" means for this study. There is a 97% chance that a runner over the age of 50 will die. We are 97% confident that fewer than 3% of people over the age of 50 are runners. ○ We are 97% confident that the population proportion of runners over the age of 50 that will die in the next eight years is between the interval values. ○ We are 97% confident that the number of deaths of runners over the age of 50 is less than 3 people.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 4AGP

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