Solution:
Confidence Interval for population proportion(p)
Given,
n = 50 ....... Sample size
x = 35 .......no. of successes in the sample
Let
denotes the sample proportion.
= x/n = 35/50 = 0.70
Our aim is to construct 95% confidence interval.
c = 0.95
= 1- c = 1- 0.95 = 0.05
/2
= 0.05
2 = 0.025 and 1-
/2 = 0.975
Search the probability 0.975 in the Z table and see corresponding z value
= 1.96 for the 95% Confidence interval
Now , confidence interval for population proportion(p) is given by:
0.70 -1.96*
0.70 +1.96*
0.70 - 0.12702251768 <
< 0.70 + 0.12702251768
0.5730 <
< 0.8270
is the required 95% confidence interval for the population proportion.
Answer is (0.5730,0.8270)
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