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A report on 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 175 adult Americans age 18 to 29 and a representative sample of 450 adult Americans age 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 36 of those in the 50 to 64 age group believed this USE SALT a Are the sample sizes large enough to use the large sample confidence interval to estimate the difference in the population proportions Explain Let p 0 48 and p 0 36 n 175 and n 450 where the 1 subscript indicates the age 18 29 group and the 2 subscript indicates the age 50 64 group Since n p n P and n 1 B all at least 10 the sample sizes are 7 p are sample confidence interval b Estimate the difference in the proportion of adult Americans age 18 to 29 who believe the foods made with genetically modified ingredients are bad for their health and the corresponding proportion for adult Americans age 50 to 64 Use a 90 confidence interval Use p P Enter your answer using interval notation Round your numerical values to four decimal places c Is zero in the confidence interval Yes o No 8 large enough to use the large What does this suggest about the difference in the two population proportions It is not plausible that the two population proportions are equal but it is unclear which proportion is higher It is highly likely that the true proportion is higher for adult Americans age 18 to 29 OIt is plausible that the two population proportions could be equal OIt is highly likely that the true proportion is higher for adult Americans age 50 to 64

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