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.**

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