Question

***Please solve the problem below using R, and provide the R code you used in order to do so. Please show all work.***

A survey of 200 people found that 128 people stated that they were trying to avoid trans fats in their diets.

a) Find the 95% confidence interval of the true proportion of people who are trying to avoid trans fats in their diets.

b) A researcher claims that at least 60% of people are trying to avoid trans fats in their diets. At the level of 0.05, is there enough evidence to reject the researcher's claim?

Answer 1

yes , this is the enough evidence to reject the researchers claim.

R Console > n 200 >x 128 > p-x/n:p [1] 0.64 #a) 95%C.I of true proportion of people who are trying to avoid trans fats > lowerl-p- (qnorm (0.975) sqrt (p* (1-p) /200)):1owerl [11 0.5734766 > upperl-p+ (qnorm (0.975) sqrt (p* (2-p)/200)) upperi [1] 0.7065234 > #b) Hypothesis HO: P0 0.60 vs Hl:PO 0.60 alpha 0.05 >#Test statistics Z (p-0.60) / (sqrt (0.60*0.40/200)) : 2 [1] 1.154701 #here Zalpha/2=1.96 #conclusion: Here Zcal<Ztable (1.96) hence we accept HO