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According to a report publish by the pew research center in Feb, 2010, 61% of Mi8llienials (american in their teens and 20's) think that their generations has a unique and distinctive identity (N-527)

a. Calculate the 95% confidence interval to estimate the percentage of melenials who believe that their generations has a distinctive identity as compared with other generations (generations X,, baby boomers or silent generations)

b. calculate the 99% confidence interval

c. Are both these results compatible with the conclusion that the majority of millenials believe that they have a unique identity that separates them from the previous generations?

Explanation / Answer

a.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Sample Size(n)=527
Sample proportion = x/n =0.61
Confidence Interval = [ 0.61 ±Z a/2 ( Sqrt ( 0.61*0.39) /527)]
= [ 0.61 - 1.96* Sqrt(0) , 0.61 + 1.96* Sqrt(0) ]
= [ 0.568,0.652]

b.
AT 99% C.I
Confidence Interval = [ 0.61 ±Z a/2 ( Sqrt ( 0.61*0.39) /527)]
= [ 0.61 - 2.576* Sqrt(0) , 0.61 + 2.58* Sqrt(0) ]
= [ 0.555,0.665]

c.
Yes, because the intervals achive higher value than stated in earlier

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