Is a Car a Necessity? A random sample of n = 1483 adults in the US were asked wh

Question

Is a Car a Necessity? A random sample of n = 1483 adults in the US were asked whether they consider a car a necessity or a luxury, 1 and we find that a 95% confidence interval for the proportion saying that it necessity is 0.83 to 0.89. Explain the meaning of this confidence interval in the appropriate context. O 95% of all adults believe a car is a necessity, with probability 0.83 to 0.89. O we are 95% sure that the proportion of all adults in the US who think a car is a necessity is between 0.83 and 0.89 O we are 95% sure that between 0.83 and 0.89 of the 1483 adults in the survey believe that a car is a necessity 0 we are 95% sure that the confidence interval for the proportion believing a car is a necessity is between 0.83 and 0.89 1Taylor P. and wang w "The Fading Glory of the Television and Telephone," Pew Research Center, http://pew ocialtrends.org/pubs/762/fading glory television telephone luxury-necessity#prc- jump, accessed August 19, 2010

Explanation / Answer

To interpret a confidence interval we have to remember that the sample information is random but there is a pattern if we look at all possible samples. Each possible sample gives us a different sample proportion and a different interval. But even though the results vary from sample to sample , we are "confident" because the margin -of -error would be satisfied for 95% of the sample.

The margin of error would be satisfied means that the interval includes the true population value.

As we have given that a 95% confidence interval for the proportion saying that car is a necessity is 0.83 to 0.89 it means,

WE ARE 95% SURE THAT THE PROPORTION OF ALL ADULTS IN THE US WHO THINK A CAR IS A NECESSITY IS BETWEEN 0.83 AND 0.89.

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