5. According to Gallup Institute (http://gallup.com), 45.5% of economically acti

Question

5. According to Gallup Institute (http://gallup.com), 45.5% of economically active adult population of the U.S. has a good job (30+ work hours per week with a regular paycheck), based upon Gallup’s daily tracking poll with 1,000 randomly selected people, conducted on December 3, 2016.

(a) Find the 99% lower confidence bound.

(b) Fill in the blanks and explain your reasoning. The use of the curve was more appropriate for this problem than curve, because ——— ——— ————————————————————————————————————————

Explanation / Answer

Answer to part a)

Formula of lower confidence bound is:

p^ - z* SE

.

SE = sqrt(p^*(1-p^)/n)

.

We got p^ = 0.455 ( or 45.5%)

n = 1000

.

z value for 99% confidence level is : 2.58

.

On plugging the values we get:

0.455 - 2.58 * sqrt(0.455*0.545/1000) , 0.455 + 2.58 * sqrt(0.455*0.545/1000)

0.4144 , 0.4956

Thus the lower bound is 0.4144

.

Answer to part b)

We made use of normal curve in this question because , it is a question related to Proportions , and the conditions of proportions are as follows:

.

we got n =1000 , p = 0.455

np = 1000 *0.455 = 455 > 10

n(1-p) = 1000 * 0.545 = 545 > 10

.

Thus both the conditions are satsified , hence the use of normal curve is justified for this problem

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