Homework Help is Here – Start Your Trial Now!
Math
Probability
Let the following numbers represent the order statistics ₁, 2, ,927 of the n 27 observations obtained in a random sample from a certain population of incomes (measured in hundreds of dollars): = 261 269 271 274 279 280 283 284 286 287 292 293 296 300 304 305 313 321 322 329 341 343 356 364 391 417 476 (i) Let Fy be the cumulative distribution function (CDF) of this population. Give a 95%

Let the following numbers represent the order statistics ₁, 2, ,927 of the n 27 observations obtained in a random sample from a certain population of incomes (measured in hundreds of dollars): = 261 269 271 274 279 280 283 284 286 287 292 293 296 300 304 305 313 321 322 329 341 343 356 364 391 417 476 (i) Let Fy be the cumulative distribution function (CDF) of this population. Give a 95%

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question

Please show me the question of 4 and 5

Let the following numbers represent the order statistics y₁, 92,927 of the n = 27 observations obtained in a random sample from a certain population of incomes (measured in hundreds of dollars): 261 269 271 274 279 280 283 284 286 287 292 293 296 300 304 305 313 321 322 329 341 343 356 364 391 417 476 (i) Let Fx be the cumulative distribution function (CDF) of this population. Give a 95% confidence interval for p = Fx (350) based on the given sample. (ii) Give a point estimate for the 80th percentile of this population, To.8, based on the given sample. (iii) Suppose we use (yi, yj) as an interval estimate for 70.8. Express the approximate confidence level for this interval in the form P(70.8 € (Y₁, Yj)) ≈ P(N(0, 1) = [a, b]) where a, b are expressions involving i, j. To achieve a given confidence level 1 - a, we may set a = -a/2, b = a/2 in the equation above. Solve for i and j in terms of Za/2. (iv) Follow this procedure to give an approximate 95% confidence interval for 0.8 based on the given sample. (Round i and j to nearest integer.) (v) Compute the exact confidence level of the interval you found in the previous part. (You probably want to use a computer for this.)
Transcribed Image Text:Let the following numbers represent the order statistics y₁, 92,927 of the n = 27 observations obtained in a random sample from a certain population of incomes (measured in hundreds of dollars): 261 269 271 274 279 280 283 284 286 287 292 293 296 300 304 305 313 321 322 329 341 343 356 364 391 417 476 (i) Let Fx be the cumulative distribution function (CDF) of this population. Give a 95% confidence interval for p = Fx (350) based on the given sample. (ii) Give a point estimate for the 80th percentile of this population, To.8, based on the given sample. (iii) Suppose we use (yi, yj) as an interval estimate for 70.8. Express the approximate confidence level for this interval in the form P(70.8 € (Y₁, Yj)) ≈ P(N(0, 1) = [a, b]) where a, b are expressions involving i, j. To achieve a given confidence level 1 - a, we may set a = -a/2, b = a/2 in the equation above. Solve for i and j in terms of Za/2. (iv) Follow this procedure to give an approximate 95% confidence interval for 0.8 based on the given sample. (Round i and j to nearest integer.) (v) Compute the exact confidence level of the interval you found in the previous part. (You probably want to use a computer for this.)
Suppose a new drug is available for treating high blood pressure. We want to investigate its effect by running a controlled experiment: . We randomly select some patients with high blood pressure and randomly divide them into two groups, Group A and Group B. 1 ● We then give the actual drug to patients in Group A and a placebo (i.e. non-harmful fake drug) to patients in Group B. Let X be the amount of blood pressure reduction in a patient taking the new drug, and Y the amount of blood pressure reduction in a patient taking the placebo. Assume that X Nux, 12) and Y~ N(μy, 8). How many patients (in total) do we need to select for participation in this experiment, if we want to construct a 95% confidence interval for "xy with length < 2?
Transcribed Image Text:Suppose a new drug is available for treating high blood pressure. We want to investigate its effect by running a controlled experiment: . We randomly select some patients with high blood pressure and randomly divide them into two groups, Group A and Group B. 1 ● We then give the actual drug to patients in Group A and a placebo (i.e. non-harmful fake drug) to patients in Group B. Let X be the amount of blood pressure reduction in a patient taking the new drug, and Y the amount of blood pressure reduction in a patient taking the placebo. Assume that X Nux, 12) and Y~ N(μy, 8). How many patients (in total) do we need to select for participation in this experiment, if we want to construct a 95% confidence interval for "xy with length < 2?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer