Estimate the true proportion of freshman business majors

Question

It has been reported that 20.4% of incoming freshmen indicate that they will major in business or a related field. A random sample of 320 incoming college freshmen were asked their preference, and 61 replied that they were considering business as a major.

Estimate the true proportion of freshman business majors with 94%confidence. Round intermediate calculations to three decimal places and final answers to one decimal place.

Answer 1

the sample proportion is:

61/320 = 0.190625 or just over 19%

the test statistic is (20%-19%)/ sqrt ( 19%*81%/ 320)

= 0.01/0.02193028727582016879038642969977

< 0.456

The sample is statistically consistent with the statement