The graph shows the results of a survey of adults in Country A, ages 33 to 51, w

Question

The graph shows the results of a survey of adults in Country A, ages 33 to 51, who were asked if they participated in a sport. Seventy percent of adults said they regularly participated in at least one sport, and they gave their favorite sport. You randomly select 200 people in Country A, ages 33 to 51, and ask them if they regularly participate in at least one sport. You find that 60% say no. How likely is the result? Do you think this sample is a good one? Explain your reasoning. Select the correct choice below and fill in the answer box within your choice. (Round to four decimal places as needed.) A. The result is highly unlikely because its probability, , is less than 0.05. Thus, the sample is not a good representative sample. B. The result is highly likely because its probability, , is greater than 0.05. Thus, the sample is not a good representative sample. C. The result is highly unlikely because its probability, , is greater than 0.05. Thus, the sample is a good representative sample. D. The result is highly likely because its probability, , is loss than 0.05. Thus, the sample is not a good representative sample.

Explanation / Answer

here p=0.70

here n=200

therefore std error =(p(1-p)/n)1/2 =0.0324

hence probabilty that 60 % say No or 40% say Yes(phat=0.4) =.P(p<0.4)=P(Z<(0.4-0.7)/0.0324)=P(Z<-9.2582)

=0.0000

therefore option A is correct. the result is highly unlikely because the probability 0.0000 is less then 0.05 ; the sample is not a good representative sample

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