A survey was conducted at local colleges around Madison, Wisconsin to find out the average height of a college student. Of 692 students surveyed, 421 replied that they were over 6 feet tall.What is the standard error? Answer choices are rounded to the hundredths place.a.)12.84b.)0.24c.)0.02d.)0.49
Question
A survey was conducted at local colleges around Madison, Wisconsin to find out the average height of a college student. Of 692 students surveyed, 421 replied that they were over 6 feet tall.What is the standard error? Answer choices are rounded to the hundredths place.a.)12.84b.)0.24c.)0.02d.)0.49
Solution
To calculate the standard error, we first need to find the proportion (p) of students who are over 6 feet tall and the proportion who are not (q).
p = 421 / 692 = 0.608
q = 1 - p = 1 - 0.608 = 0.392
The formula for the standard error (SE) for a proportion is:
SE = sqrt [ p(1 - p) / n ]
where n is the number of students surveyed.
Substituting the values we have:
SE = sqrt [ 0.608 * 0.392 / 692 ]
Calculating this gives us a standard error of approximately 0.018, which is closest to answer choice c.) 0.02 when rounded to the hundredths place.
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