Greece has faced a severe economic crisis since the end of 2009. A Gallup poll s

Question

Greece has faced a severe economic crisis since the end of 2009. A Gallup poll surveyed 1,000 randomly sampled Greeks in 2011 and found that 25% of them said they would rate their lives poorly enough to be considered "suffering." a) Define the population parameter of interest. What is the point estimate for this parameter? b) Check that the conditions required for constructing a Confidence Interval based on these data are met. c) Construct a 95% Confidence Interval for the proportion of Greeks who are "suffering." d) Describe what would happen to this Confidence interval if we decided to use a higher confidence level. e) Describe what would happen to the Confidence Level if we used a larger sample.

Explanation / Answer

(a)

Population parameter is the proportion of people saying that they are suffering.

(c)

Sample proportion, p' = 25% = 0.25

Sample size, n = 1000

Sample standard deviation, S = ( n*p'*(1-p') )0.5 = 13.69

For 95% C.I., critical z-score = zc = 1.96

So, 95% C.I. is:

0.25 - zc*(S/n0.5) < p < 0.25 + zc*(S/n0.5)

Putting values we get:

0.25 - 1.96*(13.69/10000.5) < p < 0.25 + 1.96*(13.69/10000.5)

So,

-0.598 < p < 1.098

(d)

For a higher confidence interval level, the interval range would increase since the critical z-score would increase as well.

(e)

For a larger sample size, the interval width decreases because the standard error decreases.

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