*** *** *** *** *** brand *** *** must plan a campaign *** to increase brand recognition.
He wants to *** determine *** percentage *** *** who have *** of the brand. How many adults *** *** *** *** to be 90 *** condent *** his estimate *** *** six *** points *** *** true *** *** nothing *** known *** the *** of adults *** have heard of *** *** (Round up *** *** *** *** *** *** recent survey *** that *** 76 *** *** adults have heard of the *** *** up *** *** nearest integer.)
Solution
The *** to *** the sample *** *** to estimate *** proportion *** *** p)
z E
2
where *** the proportion *** success, *** the *** *** *** margin of *** *** *** *** *** 0:06. *** condence *** is0:9. If no *** were available for
the proportion of *** *** *** *** *** the *** *** assume *** the proportion *** *** 0 *** *** critical *** of *** *** *** 1
:645 *** minimum sample *** *** to estimate the proportion is
n= p(1 *** E
2
= *** :5(1 0:5)
1:645 0
:06 *** 187 :918
188 :
Thus, *** *** *** sizen= 188will ensure *** *** condence interval *** *** *** will have a
margin of error *** .
(b)
Given *** margin of errorE= *** *** condence coecient is1 *** *** The sample proportion
of adults *** *** heard of the brand is *** 0 :76 .
The *** *** *** ZisZ
= *** *** *** .
The *** *** *** required *** *** *** proportion *** *** *** E
2
= *** *** ***
1:645 ***
2
= 137 *** 138 *** the *** of *** *** *** that the90% condence interval for *** proportion *** *** *** of *** *** .
1