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 121 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. 20.66% (25/121) 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 25/121. ? C. If another random sample of 121 Gastown residents drawn, there is a 95% probability the sample proportion of Gastown residents who are living below the poverty line equals 25/121. D. If many random samples of 121 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. E. If many random samples of 121 Gastown residents are drawn, 95% of the resulting confidence intervals will contain the value 25/121. ?
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 121 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. 20.66% (25/121) 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 25/121. ? C. If another random sample of 121 Gastown residents drawn, there is a 95% probability the sample proportion of Gastown residents who are living below the poverty line equals 25/121. D. If many random samples of 121 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. E. If many random samples of 121 Gastown residents are drawn, 95% of the resulting confidence intervals will contain the value 25/121. ?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 30E
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Transcribed Image Text:TRefer 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 121 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. 20.66% (25/121) 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 25/121. ?
C. If another random sample of 121 Gastown residents is drawn, there is a 95% probability that the sample proportion of Gastown residents who are living below the poverty line equals 25/121.
?
?
D. If many random samples of 121 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.
E. If many random samples of 121 Gastown residents are drawn, 95% of the resulting confidence intervals will contain the value 25/121. ?
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