475 / 762
Chapter 11: Confidence Intervals – Large Samples
475
Solution:
The sample proportion
̂
= 0.74 and the standard deviation for
the sample proportion
̂
=
√ ̂
̂
= 0.0310. (Verify).
Since we need to find the 95% confidence interval estimate,
= 5% = 0.05
and
= 0.05/2 = 0.025. Thus
⁄
= 1.95996. You can use the
Inverse
Normal Distribution
workbook to determine the
value. Remember, you
will have to enter the value of 0.025 in the Area column.
Thus, the 95% confidence interval estimate for the proportion of people who
do not use a consumer ratings publication when purchasing a new vehicle,
using the formula, is 0.74
1.95996
0.0310 = 0.74
0.0608.
That is, we are 95% confident that the true proportion of people who do not
consult a consumer guide when purchasing a new vehicle will be between
0.6792 and 0.8008 (to four decimal places) or between 67.92% and 80.08%.
We can use the
Large Sample Confidence Interval for a Single Population
Proportion
workbook to help with the computations.
Figure 11-6
shows a
portion of the output. It shows that the 95% confidence interval the
proportion of people who do not use a consumer ratings publication when
purchasing a new vehicle is between 0.6792 and 0.8008 to four decimal
places.