Question

In a random sample of 62 professional actors, it was found that 40 were extroverts. Please find the point estimate, 95% confidence interval for p, and provide a brief explanation of your answers.

Answer 1

The point Estimate is 0.645 , the confidence interval is (0.525 ,0.764).

What is Point Estimate ?

The point estimate is the proportion of success in the sample.

From the data given

p = 40/62

p = 0.645

The point Estimate is 0.645

(b) Confidence interval for true proportion is

$\rm {p -Z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}} , p +Z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}$

For 95 % Z = 1.96

p =0.645

1-p = 0.355

putting the values

$\rm {0.645 -1.96 \sqrt{\dfrac{0.645\times0.355}{62}} , {0.645 +1.96 \sqrt{\dfrac{0.645\times0.355}{62}}$

(0.525 , 0.764)

Lower Limit = 0.525

Upper Limit = 0.764

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