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Procter & Gimple Soap Corp. need to know the advertising medium that gives a brand the most credibility in influencing brand decisions? According to a 2 year old census of the population, 41% of Millennials indicated that TV was best. Complete parts (a) through (e).

a.  sample size needed to 95% confidence interval and margin of error of +/- 0.09. 

b.  the sample size needed for 99% confidence interval and margin of error of +/- 0.09. 

c.  Find the sample needed to construct the 95% confidence interval with a margin of error os +/- 0.09. 

d. Find the sample size needed to construct the 99% confidence interval with a margin of error of +/- 0.09. 

. Discuss the effects of changing the desired confidence level and the acceptable sampling error on sample size requirements. Select all that apply.


The problem is about construction of the confidence interval for the population proportion, normal distribution and the formulae for proportion sample size is applied. 

n = p_hatch*q_hatch(Zc/E)^2

a. When the confidence interval needed is 95% and the margin of error is +/- 0.09, 
The required sample size is;- 

=NORM.S.INV(1-0.05/2) = 1.96 (Excel is so powerful with statistical tools)

n = 0.41*0.59 * (1.96/0.09)^2 = 115 (The sample size is always rounded up to the nearest whole number)


Sample size when the confidence interval is 99% and the margin of error is +/- 0.09

=NORM.S.INV(1-0.01/2) = 2.58

n = 0.41 * 0.59 *(2.58/0.09) =  199 (Sample size rounded up)

What does increasing the confidence interval do to the required sample size?

Increasing the confidence interval increases the sample size needed this is because of the precision needed when constructing intervals with lower values of alpha.  


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