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 123 people living in Gastown and finds that 21 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. 17.07% (21/123) 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 21/123. C. If another random sample of 123 Gastown residents is drawn, there is a 95% probability that the sample proportion of Gastown residents who are living below the poverty line equals 21/123. D. If many random samples of 123 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 123 Gastown residents are drawn, 95% of the resulting confidence intervals will contain the value 21/123.
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 123 people living in Gastown and finds that 21 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. 17.07% (21/123) 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 21/123.
C. If another random sample of 123 Gastown residents is drawn, there is a 95% probability that the sample proportion of Gastown residents who are living below the poverty line equals 21/123.
D. If many random samples of 123 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 123 Gastown residents are drawn, 95% of the resulting confidence intervals will contain the value 21/123.
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