Question

The report "The New Food Fights: U.S. Public Divides Over Food Science" states that younger adults are more likely to see foods with genetically modified ingredients as being bad for their health than older adults. This statement is based on a representative sample of 178 adult Americans aged 18 to 29 and a representative sample of 427 adult Americans aged 50 to 64. Of those in the 18 to 29 age group, 48% said they believed these foods were bad for their health, while only 3% of those in the 50 to 64 age group believed this.

(a) Are the sample sizes large enough to use the large-sample confidence interval to estimate the difference in the population proportions?
(b) Estimate the difference in the proportion of adult Americans aged 18 to 29 who believe the foods made with genetically modified ingredients are bad for their health and the corresponding proportion for adult Americans aged 50 to 64. Use a 90% confidence interval.
(c) Is zero in the confidence interval?

Answer 1

a) yes

b) ( 0.0280 , 0.1720 )

c) No

Explanation:

A) Determine if the sample sizes are large enough

where :

ages between ( 18 to 29 )

p1 = 0.48 ,

n1 = 178 , ∴ n1 P1 = 85.44 also n1 ( 1 - p1 ) = 92.56

ages between ( 50 to 64 )

P2 = 0.03 ,

n2 = 427 ∴ n2p2 = 12.81 also n2( 1 -p2 ) = 414.19

since all the values ae above 10 we can conclude that the sample sizes are large enough

answer = yes

B) Estimate the difference in the proportion of adult Americans aged 18 to 29

= ( 0.0280 , 0.1720 )

attached below is the detailed solution

C) zero is not included in the interval