Question

PROBLEM 5. 20 Construct the 95 percent Confidence intervals for the following cases, state any needed assumptions, and give interpretation
n1 = 9 X1 bar = 75 sigma1 = 5, n2=9 X2 bar = 70 sigma2 = 3
Among 100 females 60 like Sports, Among 50 males 40 like sports
Find Confidence interval for p1 – p2, where p1 is true proportion of women that like sports.

Answer 1

Confidence interval(in %) = 95
z @ 95.0% = 1.96
Since we know that

Required confidence interval = (5.0-3.8096, 5.0+3.8096)
Required confidence interval = (1.1904, 8.8096)



Total number of sample 1 (n₁) = 100
Total number of sample 2 (n₂) = 50
number of favourable events (X₁) = 60
number of favourable events (X₂) = 40

Confidence interval(in %) = 95

Required Confidence interval = (-0.2 - 1.96(0.0748), -0.2 + 1.96(0.0748))
Required Confidence interval = (-0.2 - 0.1466, -0.2 + 0.1466)
Required Confidence interval = (-0.3466, -0.0534)
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