The proportion who smoke among adult residents of Kentucky in 2004 was 0.276, the highest of any state in the United States. Treat this as the population proportion, and suppose you take a random sample of 300 Kentucky residents.
a. Determine the probability of obtaining a sample proportion of Kentucky smokers that is more than 0.025 away from the population proportion (in other words, either greater than 0.301 or less than 0.251).
Round your answer to four decimal places.
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b. Repeat part a with a distance of 0.05 instead of 0.025.
Round your answer to four decimal places.
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c. If you are presented with a random sample of 300 residents from an unknown state, and you find that 25 % of the sample are smokers, would you have reason to believe that the state is not Kentucky? Explain, based on your calculation in part a.
Round your answer to the nearest integer.
There
Entry field with correct answer isis no reason to doubt that the state is Kentucky because part a shows that if the state is Kentucky, you have
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% chance of finding a sample result of at least 25 % smokers.
d. Repeat part c if you find that 22.5 % of the sample are smokers. Explain, based on your calculation in part b.
Round your answer to one decimal place.
There
Entry field with correct answer is nois reason to doubt that the state is Kentucky because part b shows that if the state is Kentucky, you have
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% chance of finding a sample result of at least 22.5 % smokers.