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How would you explain 95% confidence to a layman? Suppose a professor of IIMA thinks that true proportion is 0.3. Are you ready to accept the professor’s perception based on your data at 99% confidence level?

Solution – 1

Sample Size n = 100 (male smokers) p = 0.2

Sd (P) = √(pq / n) = .04

95% confidence interval of p

= 0.2 ± 2 x 0.04

= 0.08 to 0.32

Explanation to a layman – 95% confidence means that if the sampling experiment i.e. selection of random samples of 100 male smokers in the present problem, is repeated large no of times, 95% of the times the interval will include the true value of p (0.2) or the sample proportion of smokers in present example and 5% of the times the interval may not include the true value of p (0.2) or the sample proportion of smokers in present example.

99 % confidence interval of p

= 0.2 ± 2.58 x .04

= .04 to 0.35

Based on our data, as the true proportion of 0.3 thought by the IIMA professor lies in the 99% confidence interval, we can accept IIMA Professor’s…...

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