PROBLEM 5. 20 Construct the 95 percent Confidence intervals for the following cases, state any needed...

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.

Solutions

Expert Solution

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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orchestra answered 1 year ago

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