Question

In: Statistics and Probability

In a random sample of 61 professional actors, it was found that 48 were extroverts. Find...

In a random sample of 61 professional actors, it was found that 48 were extroverts. Find a 99% confidence interval for p.

Solutions

Expert Solution

Solution :  

Given that,

n = 61

x = 48

Point estimate = sample proportion = = x / n = 48 / 61 = 0.787

1 - = 1 - 0.787 = 0.123

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 * (((0.787 * 0.213) / 61)

= 0.135

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.787 - 0.135 < p < 0.787 + 0.135

0.652 < p < 0.922

The 99% confidence interval for the population proportion p is : 0.652 , 0.922


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