Question

In a random sample of 506 judges, it was found that 283 were introverts.

P= .5593

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

a1. lower limit

a2. upper limit

b. Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration.

A. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

B. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.   

C. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal.

D. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.

Answer 1

Solution :

Given that,

n = 506

x = 283

Point estimate = sample proportion = = x / n = 283 / 50 6 = 0.56

1 - = 0.44

Z_/2 = 2.576

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

= 2.576 * (((0.56 * 0.44) / 506)

= 0.06

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.56 - 0.06 < p < 0.56 + 0.06

0.50 < p < 0.62

Lower limit = 0.50

Upper limit = 0.62

A. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.