Example 3
In a survey conducted by a polling company, 1100 adult Americans were asked how many hours they
worked in the previous week. Based on the results, a 95% confidence interval for the mean numbers of
hours worked had a lower boung of 42.7 and an upper bound of 44.5. Provide two recommendations
for increasing the precision of the interval.
**Decrease the confidence level.
**Increase the sample size.
(Read pages 407-408)
Example 4
A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose
for a random sample of 960 people age 15 or older, the mean amount of time spent eating or drinking
per day is 1.62 hours with a standard deviation of 0.65 hour.
a) A histogram of time spent eating/drinking each day is skewed right. Use this result to explain
why a large sample is needed to construct a confidence interval for the mean.
*Since the distribution is skewed right (not normally distributed) the sample must be large so
that the distribution of the same mean will be approximately normal.
b) In 2010, there were over 200 million people nationally age 15 or older. Explain why this, along
with the fact that our data is from a random sample, satisfies the requirements for constructing
a confidence interval.
*The sample size is less than 5% of the population (n < 0.05N)
c) Determine and interpret a 95% confidence interval for the mean amount of time Americans age
15 or older spend eating/drinking each day.
gives us this:
Rounded to two places, the interval is (1.58, 1.66)
Which means the nutritionist can be 95% confident that the mean amount of time Americans spend
eating/drinking per day is between 1.58 and 1.66 hours.