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In a certain state, a survey of 600 workers showed that 35% belonged to a union. Find the 95% confidence interval of true proportion of workers who belong to a union.

Sagot :

Answer:

The 95% confidence interval of true proportion of workers who belong to a union.

(0.29657 , 0.40343)

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 600

Given sample proportion  p = 35% or 0.35

The 95% confidence interval of true proportion of workers who belong to a union.

[tex](p^{-} -Z_{0.05} \sqrt{\frac{pq}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{pq}{n} } )[/tex]

[tex](0.35 -1.96\sqrt{\frac{0.35 X0.65}{600} } , 0.35 + 1.96\sqrt{\frac{0.35 X 0.65}{600} } )[/tex]

( 0.35 - 1.96 (0.02726) , 0.35 + 1.96 (0.02726)

(0.35 - 0.05343 , 0.35 + 0.05343)

(0.29657 , 0.40343)

Final answer:-

The 95% confidence interval of true proportion of workers who belong to a union.

(0.29657 , 0.40343)