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.

E.) Describe what would happen to the Confidence Level if we used a larger sample

Answer 1

A)

The population parameter of interest is proportion of Greeks who rate their lives poorly enough to be considered "suffering."

The point estimate for this parameter is 0.25

B)

n = 1000, p = 0.25

np = 1000 * 0.25 = 250

n(1-p) = 1000 * (1 - 0.25) = 750

Thus, both np and n(1-p) are greater than 10. Thus, the conditions required for constructing a Confidence Interval based on these data are met.

C)

Standard error of sample proportion =

Z value for 95% Confidence Interval is 1.96

Margin of error = Z * Standard error = 1.96 * 0.0137 = 0.026852

95% Confidence Interval for the proportion of Greeks who are "suffering." is,

(0.25 - 0.026852, 0.25 + 0.026852)

(0.223148, 0.276852)

D)

With higher confidence, the Z value would increase and correspondingly the margin of error would increase. Thus, the length of Confidence Interval would increase. (Length of Confidence Interval is difference between upper and lower bound of the interval which is 2 * Margin of error)

E)

For large sample (n), standard error would decrease and and correspondingly the margin of error would decrease. Thus, the length of Confidence Interval would decrease. (Length of Confidence Interval is difference between upper and lower bound of the interval which is 2 * Margin of error)