Question

Determine the margin of error for a confidence interval to estimate the population proportion for the following confidence levels with a sample proportion equal to

0.45 and n equals=120.

a. 90​%

b. 95​%

c. 99​%

Answer 1

Solution :

Given that,

a.

Point estimate = sample proportion = = 0.45

1 - = 1 - 0.45 = 0.55

Z/2 = 1.645

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

= 1.645 * (((0.45 * 0.55) / 120)

Margin of error = E = 0.075

b.

Point estimate = sample proportion = = 0.45

1 - = 1 - 0.45 = 0.55

Z/2 = 1.96

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

= 1.96 * (((0.45 * 0.55) / 120)

Margin of error = E = 0.089

c.

Point estimate = sample proportion = = 0.45

1 - = 1 - 0.45 = 0.55

Z/2 = 2.576

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

= 2.576 * (((0.45 * 0.55) / 120)

Margin of error = E = 0.117