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In: Statistics and Probability

Life rating in Greece. Greece faced a severe economic crisis since the end of 2009. Suppose...

Life rating in Greece. Greece faced a severe economic crisis since the end of 2009. Suppose a Gallup poll surveyed 1,000 randomly sampled Greeks in 2011 and found that 26% of them said they would rate their lives poorly enough to be considered "suffering." Round all answers to two decimal places.

1. What is the population parameter of interest?
A. The 25% of Greeks in the sample who believe they are suffering.
B. The score on the survey that corresponds to suffering.
C. The actual proportion of Greeks who believe they are suffering.
D. All the people who live in Greece.

2. What is the value of the point estimate of this parameter?

3. Construct a 95% confidence interval for the proportion of Greeks who are "suffering." ( , )

4. If we decided to use a higher confidence level, the confidence interval would be:
A. narrower
B. wider
C. stay the same

5. If we used the same confidence level with a larger sample, the confidence interval would be:
A. wider
B. narrower
C. stay the same

Solutions

Expert Solution

1) Answer is C. (i.e) The actual proportion of Greeks who believe they are suffering

Solution:The population parameter of interest is the proportion of all Greeks who would rate their lives poorly enough to be considered suffering, p. The point estimate for this parameteris the proportion of Greeks in this sample who would rate their lives as such, ˆp= 0.25.

2) Ans: The population parameter of interest is the proportion of all Greeks who would rate their lives poorly enough to be considered suffering, p. The point estimate for this parameteris the proportion of Greeks in this sample who would rate their lives as such, ˆp= 0.25.

3) Solution: A 95% confidence interval can be calculated as follows:

We are 95% confident that approximately 23% to 29% of Greeks would rate their lives poorlyenough to be considered suffering

4) Answer is B. Wider

Solution: Increasing the confidence level would increase the margin of error hence wider the Intervel.

5) Answer is B Narrower

Solution: Increasing the sample size would decrease the margin of error hence make the in-terval narrower.

orchestra answered 2 years ago
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