The Gallup Organization released the results of a poll concerning the American a

Question

The Gallup Organization released the results of a poll concerning the American attitudes toward the Winter Olympic Games. The poll results were based on telephone interviews with a randomly selected national sample of 1011 adults, 18 years and older.

Suppose we wish to use the poll’s result to justify the claim that more than 30 percent of Americans (18 years or older) say that figure skating is their favorite Winter Olympic event. The poll actually found that 32 percent of respondents reported that figure skating was their favorite event. Suppose we assume that 30 percent of Americans (18 years or older) say figure skating is their favorite event.

1. Describe the sampling distribution of the sample proportion of people who say figure skating is their favorite event.

2. Find the probability of observing a sample proportion of .32 or more respondents saying figure skating is their favorite event.

3. Based on the probability in question 2, would you conclude that more than 30 percent of Americans (18 or older) say that figure skating is their favorite Winter Olympic event? Explain.

Explanation / Answer

1) as sample size is high and np>10 as well n(1-p)>10 sampling distribution will be approximately normal

with mean proportion =0.3 and std error =(p(!-p)/n)1/2 =0.0144

2)P(X>0.32)=1-P(X<0.32)=1-P(Z<(0.32-0.3)/0.0144)=1-P(Z<1.3877)=1-0.9174=0.0826

3) as probabilty of above is greater then 0.05 we can not conclude that more than 30 percent of Americans (18 or older) say that figure skating is their favorite Winter Olympic event cause it is not unusual event

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