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Refer to the following scenario. A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 130 people living in Gastown and finds that 25 have an annual income that is below the poverty line. For each of the following statements, specify whether the statement is a correct interpretation of the 95% confidence interval for the true proportion of Gastown residents living below the poverty line. A. 19.23% (25/130) of Gastown residents are living below the poverty line. ? B. There is a 95% probability that the true proportion of Gastown residents who are living below the poverty line equals 25/130. ? C. If another random sample of 130 Gastown residents is drawn, there is a 95% probability that the sample proportion of Gastown residents who are living below the poverty line equals 25/130. ? ✪ D. If many random samples of 130 Gastown residents are drawn, 95% of the resulting confidence intervals will contain the value of the true proportion of Gastown residents who are living below the poverty line. 2

Refer to the following scenario. A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 130 people living in Gastown and finds that 25 have an annual income that is below the poverty line. For each of the following statements, specify whether the statement is a correct interpretation of the 95% confidence interval for the true proportion of Gastown residents living below the poverty line. A. 19.23% (25/130) of Gastown residents are living below the poverty line. ? B. There is a 95% probability that the true proportion of Gastown residents who are living below the poverty line equals 25/130. ? C. If another random sample of 130 Gastown residents is drawn, there is a 95% probability that the sample proportion of Gastown residents who are living below the poverty line equals 25/130. ? ✪ D. If many random samples of 130 Gastown residents are drawn, 95% of the resulting confidence intervals will contain the value of the true proportion of Gastown residents who are living below the poverty line. 2

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...
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Refer to the following scenario. A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 130 people living in Gastown and finds that 25 have an annual income that is below the poverty line. For each of the following statements, specify whether the statement is a correct interpretation of the 95% confidence interval for the true proportion of Gastown residents living below the poverty line. A. 19.23% (25/130) of Gastown residents are living below the poverty line. ? ↑ B. There is a 95% probability that the true proportion of Gastown residents who are living below the poverty line equals 25/130. î ? C. If another random sample of 130 Gastown residents is drawn, there is a 95% probability that the sample proportion of Gastown residents who are living below the poverty line equals 25/130. ? D. If many random samples of 130 Gastown residents are drawn, 95% of the resulting confidence intervals will contain the value of the true proportion of Gastown residents who are living below the poverty line. ? î
Transcribed Image Text:Refer to the following scenario. A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 130 people living in Gastown and finds that 25 have an annual income that is below the poverty line. For each of the following statements, specify whether the statement is a correct interpretation of the 95% confidence interval for the true proportion of Gastown residents living below the poverty line. A. 19.23% (25/130) of Gastown residents are living below the poverty line. ? ↑ B. There is a 95% probability that the true proportion of Gastown residents who are living below the poverty line equals 25/130. î ? C. If another random sample of 130 Gastown residents is drawn, there is a 95% probability that the sample proportion of Gastown residents who are living below the poverty line equals 25/130. ? D. If many random samples of 130 Gastown residents are drawn, 95% of the resulting confidence intervals will contain the value of the true proportion of Gastown residents who are living below the poverty line. ? î
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