a. determine the sample proportionb. decide whether using the one .pdf

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The document outlines steps to calculate confidence intervals for one proportion using the z-interval procedure. It provides sample data with 40 successes out of 50 trials at the 95% confidence level and 3 successes out of 100 trials at the 99% confidence level. It shows the work to calculate the confidence intervals for each case using the appropriate z-value and standard deviation formula.

Formation

a. determine the sample proportion
b. decide whether using the one proportion z interval procedure is apporapriate
c. If appropriate, use the one proportion z interval procedure to find the confidence interval at the
specified confidence level.
x=40, n=50, 95% level
x=3, n=100, 99% level
show work
Solution
(a) p=40/50=0.8
p=3/100=0.03
(b)one proportion z interval procedure is apporapriate
(c) Given a=0.05, |Z(0.025)|=1.96 (From standard normal table)
So 95% CI is
p +/- Z*v(p*(1-p)/n)
--> 0.8+/- 1.96*sqrt(0.8*0.2/50)
--> (0.6891257, 0.9108743)
Given a=0.01, |Z(0.005)|=2.58 (from standard normal table)
So 99% CI is
p +/- Z*v(p*(1-p)/n)
--> 0.8+/- 2.58*sqrt(0.8*0.2/50)
--> (0.6540532, 0.9459468)

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