A survey indicates that 26% of consumers from a certain region are willing to sp

Question

A survey indicates that 26% 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 100 consumers from the region is selected. If possible, use the normal distribution to approximate the sampling distribution of the proportion.

If a sample of400 is taken, what is the probability that in the sample between 21% and 31% are willing to spend extra for products and services from socially responsible companies?

Homework.asphomewcekid-464694908&questionld-18shed-ruedld; 48382578centen Stat 2 Spring 2018 Mchael Beale 2/1/1812 10 PM Homework: HW 1 Normal Distrib, Sampling Distrib Ch 6.2& Ch Score: 0.3 of 1 pt 7of7(1 complete) Score: 67 69%, 474 of 7 pts 7.3.15-T Asurvey racales that20% d coroners ton a certan regen ae wing to corsumers as socaly conscious consemens etam of ther cause markeing eflots Souppose a sample of 100 consusthe region is selected I the propartion Conplete parts (a) teough ig) below gerd ena tr proacts and sences from sonaly orstle cor Then-chers ann tme aras If pessièle, use the nomal dstitution to approximate the samping osatution of The poetatalee 50 % Round to two deoimal placies as needed ) Round to two decmal places as needed ) The probabilty 8728% Round to two deonal places as needed) Round to hwn decimal places as needed) The probabilty is Round to two decina places an needed ) Enter your answer in the answor box and then cick Check A

Explanation / Answer

here for population proportion p=0.26

for n=400; std error of mean =0.0219

therefore  probability that in the sample between 21% and 31% are willing to spend extra for products and services from socially responsible companies =P(0.21<P<0.31)=P((0.21-0.26)/0.0219<Z<(0.31-0.26)/0.0219)

=P(-2.2789<Z<2.2789)=.9887-0.0113 =0.9774

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