Question

Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related. The 90% confidence interval for the population proportion is _________.

Answer 1

Answer:

The 90% confidence interval for the population proportion is

(0.10872, 0.19128)

Step-by-step explanation:

Explanation:-

Step(i):-

Given data A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related

Given random sample size 'n' = 200

Given Thirty of the messages were not business related

 let 'x' = 30

Probability of the messages were not business related or proportion

$p = \frac{x}{n} = \frac{30}{200} = 0.15$

Step(ii):-

The 90% confidence interval for the population proportion is

$(p - Z_{0.10} \sqrt{\frac{p(1-p)}{n} } , p + Z_{0.10} \sqrt{\frac{p(1-p)}{n} } )$

Level of significance ∝ = 0.90 or 0.10

The critical value   Z₀.₁₀ = 1.645

The 90% confidence interval for the population proportion is

$( 0.15-1.645 \sqrt{\frac{0.15(1-0.15)}{200} } , 0.15 +1.645 \sqrt{\frac{0.15(1-0.15)}{200} } )$

on calculation, we get

(0.15 - 0.04128 , (0.15 + 0.04128)

(0.10872, 0.19128)

Conclusion:-

The 90% confidence interval for the population proportion is

(0.10872, 0.19128)