It is known that 57% of University of Georgia undergraduate students spend more

Question

It is known that 57% of University of Georgia undergraduate students spend more time browsing the internet per day than they do watching TV. We will assume that JMU students taking Math 220 this semester behave just as the U. Ga students do with respect to their internet and TV use. Find the approximate probability that we would obtain a sample of 63 JMU students in which at most 51% spend more time using the internet per day than watching TV if the true proportion of all students who spend more time using the internet per day than watching TV is 57%.

Explanation / Answer

Ans:

Sampling distribution of sample proportions:

mean=p=0.57

standard deviation=sqrt(0.57*(1-0.57)/63)=0.0624

z=(0.51-0.57)/0.0624=-0.96

P(z<=-0.96)=0.1685

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