Life rating in Greece ~ Greece faced a severe economic crisis since the end of 2009. Suppose a Gallup poll surveyed 1110 randomly sampled Greeks in 2011 and found that 266 of them said they would rate their lives poorly enough to be considered “suffering.” Round all answers to four decimal places. 1. What is the population parameter of interest? A. The score on the survey that corresponds to suffering.B. All the people who lived in Greece in 2011.C. The actual proportion of Greeks who said they were suffering in 2011.D. The 266 Greeks in the sample who believed they were suffering. 2. What is the value of the point estimate of this parameter? ?̂=p^= 3. Use the sample information from 2011 to construct a 90% confidence interval for the proportion of Greeks in 2011 who said they were “suffering.” ( , ) 4. If we decided to use a higher confidence level, the confidence interval would be: A. widerB. narrowerC. stay the same 5. If we used the same confidence level with a larger sample, the confidence interval would be: A. widerB. narrowerC. stay the same 6. The sample information from 2011 gives a standard error of ???̂=SEp^= 0.0128. Which of the statements below is a correct interpretation of the standard error? A. If we had taken many samples of size n = 1110 from the population in 2011, we would expect any of those sample proportions to be approximately 0.0128 from the true population proportion, on average.B. We have strong evidence that the true proportion of people who said they were suffering in 2011 is within the 90% confidence interval.C. We can be 1.28% confident that our margin of error is approximately correct.D. There is a 1.28% chance the sample proportion we calculated is the same as the true population proportion. 7. Suppose we wanted to take a new sample of Greeks today, ask them the same question, and calculate a 90% confidence interval for the proportion of Greeks today who say they are “suffering” with a margin of error of no more than 3.25%. What size sample should we take? Important! Use the information from the 2011 sample for a planning value for ?∗p∗ and round your ?∗z∗ value to EXACTLY 3 decimal places. Your answer should be given as an integer.

Question

Life rating in Greece ~ Greece faced a severe economic crisis since the end of 2009. Suppose a Gallup poll surveyed 1110 randomly sampled Greeks in 2011 and found that 266 of them said they would rate their lives poorly enough to be considered “suffering.” Round all answers to four decimal places. 1. What is the population parameter of interest? A. The score on the survey that corresponds to suffering.B. All the people who lived in Greece in 2011.C. The actual proportion of Greeks who said they were suffering in 2011.D. The 266 Greeks in the sample who believed they were suffering. 2. What is the value of the point estimate of this parameter? ?̂=p^= 3. Use the sample information from 2011 to construct a 90% confidence interval for the proportion of Greeks in 2011 who said they were “suffering.” ( , ) 4. If we decided to use a higher confidence level, the confidence interval would be: A. widerB. narrowerC. stay the same 5. If we used the same confidence level with a larger sample, the confidence interval would be: A. widerB. narrowerC. stay the same 6. The sample information from 2011 gives a standard error of ???̂=SEp^= 0.0128. Which of the statements below is a correct interpretation of the standard error? A. If we had taken many samples of size n = 1110 from the population in 2011, we would expect any of those sample proportions to be approximately 0.0128 from the true population proportion, on average.B. We have strong evidence that the true proportion of people who said they were suffering in 2011 is within the 90% confidence interval.C. We can be 1.28% confident that our margin of error is approximately correct.D. There is a 1.28% chance the sample proportion we calculated is the same as the true population proportion. 7. Suppose we wanted to take a new sample of Greeks today, ask them the same question, and calculate a 90% confidence interval for the proportion of Greeks today who say they are “suffering” with a margin of error of no more than 3.25%. What size sample should we take?  Important! Use the information from the 2011 sample for a planning value for ?∗p∗ and round your ?∗z∗ value to EXACTLY 3 decimal places. Your answer should be given as an integer.

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