Question

Use the sample data and confidence level given below to complete parts (a) through (d).

A research institute poll asked respondents if they acted to annoy a bad driver. In the poll, n = 2420 and x= 1043 who said they honked. Use a 90% confidence level.

a. find the best point estimate of the population proportion p (round to 3 decimal places)

b. identify the value of the margin of error E (round to 4 decimal places)

c. construct the confidence interval

d. write a statement that correctly interprets the confidence interval

A. There is a 90 % chance that the true value of the population proportion will fall between the lower bound and the upper bound.

B. One has 90 % confidence that the sample proportion is equal to the population proportion.

C. One has 90 % confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

D.90 % of sample proportions will fall between the lower bound and the upper bound

Answer 1

a. Best point estimate of the population proportion p = x / n = 1043 / 2420 = 0.431

b. Margin of error E = Z_alpha/2 * ( p * ( 1 - p ) / n )^0.5

Alpha = 1 - 0.90 = 0.10

n = 2420

Margin of error = Z_0.10/2 * ( 0.431 * ( 1 - 0.431) / 2420 )^0.5

= Z_0.05 * ( 0.431 * ( 1 - 0.431) / 2420 )^0.5

= 1.645 * ( 0.431 * ( 1 - 0.431) / 2420 )^0.5 (using standard normal tables )

Margin of error E = 0.0166

c. 90% confidence inetrval will be :

Upper bound = p + Margin of error(E) = 0.431 + 0.0166 = 0.4476

Lower bound = p - Margin of error(E) = 0.431 - 0.0166 = 0.4144

90% confidence inetrval will be : ( 0.4144 , 0.4476 )

d. Statement that correctly interprets the confidence interval :

C. One has 90 % confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.