A survey indicates that 23% of consumers from a certain region are willing to sp

Question

A survey indicates that 23% of consumers from a certain region are willing to spend extra for products and services from socially responsible companies. The researchers define these consumers as socially conscious consumers. According to one of the researchers, marketers need to know who these consumers are if they want to maximize the social and business return of their cause-marketing efforts. Suppose a sample of 200 consumers from the region is selected. If possible, use the normal distribution to approximate the sampling distribution of the proportion. If a sample of 800 is taken, what is the probability that in the sample between 18% and 28% are willing to spend extra for products and services from socially responsible companies?

Explanation / Answer

1) for n=200 ;

sampling distribution of proportion will be normal with prportion p=0.23

and std error of sample =(p*(1-p)/n)1/2 =0.0298

2)

for n=800 ;

sampling distribution of proportion will be normal with prportion p=0.23

and std error of sample =(p*(1-p)/n)1/2 =0.0149

as for normal distribution : z score =(sample proportion-population proportion)/std error

hence probability that in the sample between 18% and 28% are willing to spend extra

=P(0.18<P<0.28) =P((0.18-0.23)/0.0149<Z<(0.28-0.23)/0.0149)

=P(-3.3605<Z<3.3605)=0.9996-0.0004 =0.9992

(please revert for any clarification)

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