A survey is being conducted in a city with 1 million residents. It would be far too expensiveto survey all of the residents, so a random sample of size 1000 is chosen (in practice, thereare many challenges with sampling, such as obtaining a complete list of everyone in the city,and dealing with people who refuse to participate). The survey is conducted by choosingpeople one at a time, with replacement and with equal probabilities.(a) Explain how sampling with versus without replacement here relates to thebirthday problem.(b) Find the probability that at least one person will get chosen more than once.

A survey is being conducted in a city with 1 million residents. It would be far too expensiveto survey all of the residents, so a random sample of size 1000 is chosen (in practice, thereare many challenges with sampling, such as obtaining a complete list of everyone in the city,and dealing with people who refuse to participate). The survey is conducted by choosingpeople one at a time, with replacement and with equal probabilities.(a) Explain how sampling with versus without replacement here relates to thebirthday problem.(b) Find the probability that at least one person will get chosen more than once.

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...

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disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 223 numerical entries from the file and r = 48 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.(i) Test the claim that p is less than 0.301. Use ? = 0.05. (a) What is the level of significance?State the null and alternate hypotheses. H0: p < 0.301; H1: p = 0.301H0: p = 0.301; H1: p > 0.301 H0: p = 0.301; H1: p < 0.301H0: p = 0.301; H1: p ≠ 0.301 (b) What sampling distribution will you use? The standard normal, since np > 5 and nq > 5. The standard normal, since np < 5 and nq <…
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True or False: Suppose I conducted a study using random assignment. This suggests that I took great effort to ensure that all of my subjects had an equal chance of being in either group.
An industrial psychologist feels that a big factor in job turnover among assembly line workers is the individual employee’s self-esteem. She thinks that workers who change jobs often (Population A) have, on the average, lower self-esteem, as measured by a standardized test, than workers whodo not (Population B). To determine whether she can support her belief with statistical analysis, she draws a simple random sample of employees from each population and gives each a test measuring self-esteem. The results are as follows: Group A 60 45 42 62 68 54 52 55 44 41 Group B 70 72 74 74 76 91 71 78 76 78 83 50 52 66 65 53 52 The psychologist believes that the relevant population scores are normally distributed, with equal, although unknown, variances. At the 0.1 level of significance, what should she conclude
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