survey of 1000 randomly selected American adults 56% say they rarely or never go

Question

survey of 1000 randomly selected American adults 56% say they rarely or never go out to the movies, while 32% go "occasionally" and 12% go at least once a month. We wish to estimate the proportion of American adults that rarely or never go out to the movies, and the report tells us: "The margin of sam- pling error is +/-3 percentage points with a 95% level of confidence." Find and interpret a 95% con- fidence interval for the proportion rarely or never going out. Can we be relatively sure that the percent rarely or never going out to the movies is greater than 50%? B.26 Most Americans Don't Go Out to Movies According to a surveyl most Americans prefer to watch a movie in the comfort of their own home rather than going out to a theater. In the telephone hnpoislice.seriousears.com/erchives/201004staristical-analysis of-a-pizza-delivery-skifi-20100429 hrnl. 6]“56% Rarely Go To Movies," Rasmassen Reports, February 7, 2012

Explanation / Answer

B.26

Here the proportion of Americans who rarely or never go out for movies = 0.56

Here margin of error = 3% = 0.03 for 95% confidence.

So the 95% confidence interval = (0.53, 0.59)

So, we can interpret that confidence interval is that if we repeatedly take samples of AMerican adultl population of size 1000, then there is 95% probability that the sample proportion will lie in between 0.53 to 0.59.

so, we can see that the value of 0.50 doesn't lie in between the confidence interval so we shall say that majority of Americans don't go out for movies.

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