In: Statistics and Probability
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 534 judges, it was found
that 288 were introverts.
(a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.)
(b) Find a 99% confidence interval for p. (Round your answers to two decimal places.)
lower limit ? | |
upper limit ? |
Solution :
Given that,
n = 534
x = 288
Point estimate = sample proportion = = x / n = 288/534=0.539
1 - = 1-0.539=0.461
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 ( Using z table )
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 2.576 (((0.539*0.461) /534 )
= 0.06
A 99% confidence interval for population proportion p is ,
- E < p < + E
0.539-0.06< p < 0.539+0.06
0.483< p < 0.595
lower limit 0.48 | |
upper limit 0.60 |
Your answer