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In: Statistics and Probability

For this problem, carry at least four digits after the decimal in your calculations. Answers may...

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 502 judges, it was found that 275 were introverts

(b) Find a 99% confidence interval for p. (Round your answers to two decimal places.)

lower limit
upper limit

Expert Solution

Solution :

Given that,

n = 502

x = 275

Point estimate = sample proportion = = x / n = 275 /502 = 0.548

1 - = 1 - 0.548 = 0.452

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

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

= 2.576 ( $\sqrt$ ((0.548 * 0.452) / 502)

= 0.06

A 99% confidence interval for population proportion p is ,

± E

0.548 ± 0.06

Upper limit = 0.61

Lower limit = 0.49

orchestra answered 2 years ago

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