Question

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

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

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

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

Alpha = 1 - 0.90 = 0.10

n = 2420

Margin of error = Z0.10/2 * ( 0.431 * ( 1 - 0.431) / 2420 )0.5

= Z0.05 * ( 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.

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