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Mathematics

A survey of a random sample of 12000 adults in the US home-buying market finds that 97% of those surveyed recognized a certain real estate brand name. If the margin of error was 2.4%, of the following, which is the best estimate of the percent of adults in the home-buying market in the US who recognize this real estate brand name?

A.88%
B.92%
C.96%
D.100%

答案和解析

答案：B

解析：

Choice C is correct. If the researchers repeated the study many times with randomly selected groups of US adult participants, they would expect the true percent of adults in the home-buying market who recognize the real estate brand name to be within the margin of error around the sample proportion.

The interval around the sample statistic is called the confidence interval. In this case, that interval is 97% ± 2.4%.

97-2.4=94.6
97+2.4=99.4

It is likely that the true percent of US adults in the home-buying market who recognize the brand name would be between 94.6% and 99.4%.

Only one of the options falls within this range. Of these options, it is most likely that 96% of adults in the US home-buying market recognize the real estate brand name.