Question

A random sample of 130 observations results in 78 successes. [You may find it useful to reference the z table.]

a. Construct the an 95% confidence interval for the population proportion of successes. (Round intermediate calculations to at least 4 decimal places. Round "z" value and final answers to 3 decimal places.)

b. Construct the an 95% confidence interval for the population proportion of failures. (Round intermediate calculations to at least 4 decimal places. Round "z" value and final answers to 3 decimal places.)

Answer 1

Solution :

Given that,

(a)

Point estimate = sample proportion = = x / n = 78 / 130 = 0.60

1 - = 0.40

Z_/2 = 1.96

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

= 1.96 * (((0.600 * 0.400) /130 )

= 0084

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.600 - 0.084 < p < 0.600 + 0.084

0.516 < p < 0.684

(b)

Point estimate = sample proportion = = x / n = 52 / 130 = 0.400

1 - = 0.600

Z_/2 = 1.96

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

= 1.96 * (((0.400 * 0.600) /130 )

= 0084

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.400 - 0.084 < p < 0.400 + 0.084

0.316 < p < 0.484