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 126 people living in Gastown and finds that 24 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. 1) 19.05% (24/126) of Gastown residents are living below the poverty line. (true or false) 2) There is a 95% probability that the true proportion of Gastown residents who are living below the poverty line equals 24/126. (true or false) 3)If another random sample of 126 Gastown residents is drawn, there is a 95% probability that the sample proportion of Gastown residents who are living below the poverty line equals 24/126. (true or false) 4) If many random samples of 126 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. (true or false) 5)If many random samples of 126 Gastown residents are drawn, 95% of the resulting confidence intervals will contain the value 24/126. (true or false)
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 126 people living in Gastown and finds that 24 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.
1) 19.05% (24/126) of Gastown residents are living below the poverty line. (true or false)
2) There is a 95%
3)If another random sample of 126 Gastown residents is drawn, there is a 95% probability that the sample proportion of Gastown residents who are living below the poverty line equals 24/126. (true or false)
4) If many random samples of 126 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. (true or false)
5)If many random samples of 126 Gastown residents are drawn, 95% of the resulting confidence intervals will contain the value 24/126. (true or false)
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