Statistical Inference Examples
MATH 161A Fall 2023
Professor Gottlieb
1. A student government representative at a local university claims that 60% of the undergraduate
students favor a move to Division I in college football. A random sample of 250 undergraduate
students was selected and 140 students indicated they favored a move to Division I. Find a 95%
confidence interval for the true proportion of undergrads students who favor the move to Division
I. Can the representative’s claim be questioned based on the confidence interval?
Justify your
answer.
2. One study revealed that children under the age of 10 watch an average of 4.5 hours of television
per day. A group of families from a certain community would like to believe that their children
watch television less television than the national average. A random sample of 56 children from
the community yielded a mean of 4.1 hours per day with a standard deviation of 2.4 hours. Test
the appropriate hypotheses
α
= 0
.
01 level of significance.
3. The manufacturer of an energy drink claims the drink can keep you focused for 8 hours on aver-
age. A random sample of 41 students was selected to consume the energy drink and report the
number of hours they felt able to focus. For these students, the mean time was 7.2 hours with a
standard deviation of 1.9 hours. A competitor claims that the energy drink manufacturer’s claim
is unreasonable. Perform the appropriate test of hypothesis to determine whether the competitor
is correct.
Test using
α
= 0
.
05 and find the p-value for this test.
What would happen if you
changed to
α
= 0
.
01?
