Answer:
a
The population parameter of interest is the true proportion of Greek who are suffering
While the point estimate of this parameter is proportion of those that would rate their lives poorly enough to be considered "suffering". which is 25%
b
The condition is met
c
The 95% confidence interval is
d
If the confidence level is increased which will in turn reduce the level of significance but increase the critical value() and this will increase the margin of error( deduced from the formula for margin of error i.e ) which will make the confidence interval wider
e
Looking at the formula for margin of error if the we see that if the sample size is increased the margin of error will reduce making the confidence level narrower
Step-by-step explanation:
From the question we are told that
The sample size is n = 1000
The population proportion is
Considering question a
The population parameter of interest is the true proportion of Greek who are suffering
While the point estimate of this parameter is proportion of those that would rate their lives poorly enough to be considered "suffering". which is 25%
Considering question b
The condition for constructing a confidence interval is
So
Hence the condition is met
Considering question c
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
Next we obtain the critical value of from the normal distribution table, the value is
Generally the margin of error is mathematically represented as
substituting values
The 95% confidence interval is mathematically represented as
substituting values
substituting values
considering d
If the confidence level is increased which will in turn reduce the level of significance but increase the critical value() and this will increase the margin of error( deduced from the formula for margin of error i.e ) which will make the confidence interval wider
considering e
Looking at the formula for margin of error if the we see that if the sample size is increased the margin of error will reduce making the confidence level narrower