Suppose that administrators of a large school district wish to estimate the prop

Question

Suppose that administrators of a large school district wish to estimate the proportion of children in the district enrolling in kindergarten who attended preschool. They took a simple random sample of children in the district who are enrolling in kindergarten. Out of 60 children sampled, 39 had attended preschool Construct a large-sample 95% z-confidence interval for p, the proportion of all children enrolled in kindergarten who attended preschool. Give the limits of the confidence interval as decimals, precise to at least three decimal places lower limit upper limit: Construct a plus four 95% z-confidence interval for p. Give the limits of the confidence interval as decimals, precise to at least three decimal places. lower limit upper limit

Explanation / Answer

Here P = x / n = 39 / 60 = 0.65

95 % cofidencce interval of p

P^ - E < P < P^ + E

where , E =Zc P^ q^ /n

Zc =1.64 = 1.64 0.65 *0.35 /60
=0.0615

=0.65-0.0615 < P < 0.65 +0.0615

= 0.588423 < P > 0.711577

=0.588 < P < 0.712

95 % C.I for p is (0.588 ,0.712)

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