Suppose that administrators at a large urban high school want to gain a better u

Question

Suppose that administrators at a large urban high school want to gain a better understanding of the prevalence of bullying within their school. They select a random sample of 250 students who are asked to complete a survey anonymously. Of these students, 89 report that they have experienced bullying. Use this information to find a 90% zconfidence interval for p, the true proportion of students at this school who have experienced bullying.

Give the limits (bounds) of the confidence interval as a proportion, precise to three decimal places.

lower limit =

upper limit =

Explanation / Answer

p is 89/250=0.356 and N is 250

z for 90% confidence is 1.65

thus the lower limit is p-z*sqrt(p*(1-p)/N)=0.356-1.65*sqrt(0.356*(1-0.356)/250)=0.3060

upper limit is p+z*sqrt(p*(1-p)/N)=0.356+1.65*sqrt(0.356*(1-0.356)/250)=0.40597

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