Question

Use the following information to solve problems 11 through 12

A survey of 100 recent fatal traffic accidents showed that 60 were alcohol-related.

11. The 90% confidence interval for the population proportion is equal to:

a. (0.474, 0.726) b. (0.504, 0.696) c. (0.519. 0.681)

12. If a preliminary estimate of the population proportion is not known, then the minimum sample size necessary in order to estimate the sample proportion within 0.02 of the population proportion with 95% confidence is: a. 25

b. 1225 c. 2401

Answer 1

Solution:

Given:

Sample size = n = 100

x = Number of fatal traffic accidents were alcohol-related = 60

Question 11)

Construct a 90% confidence interval for the population proportion

Formula:

where

and

Z_c is z critical value for c = 90% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.90) / 2 = 1.90 / 2 = 0.9500

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_c = 1.645

Thus

thus

Thus correct answer is:

c. (0.519. 0.681)

Question 12)

a preliminary estimate of the population proportion is not known,

thus p = 0.5

E = Margin of error = 0.02

c = confidence level = 95%

Find sample size n

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

thus

Thus correct answer is: c. 2401