Answered

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."

Answer :

gametennis29

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

Other Questions