MA23 Exam 4
Name_____________________________
Directions: Show all your work in the spaces provided. Be sure to make a sketch,
state the null hypothesis and alternative hypothesis, find the critical value(s), test
value or test statistic, and make a conclusion.
1. A random sample of 46 adult coyotes in a region of northern Minnesota showed
the average age to be 2.05 years with sample standard deviation of 0.82 years
(based on information from the book Coyotes: Biology, Behavior and
Management by Bekoff, Academic Press). However, it is thought that the overall
population mean age of coyotes is 1.75 years. Does the sample data indicate that
coyotes in this region of northern Minnesota tend to live longer than the average
of 1.75 years? Use   0.01.
Ans. This is a z-test since we know the population standard deviation.
H 0 :   1.75; H 1: :   1.75 It is a right tail test with a critical value of 2.33.
The test value is 2.48 So there is enough evidence to reject the null
hypothesis.
2. The heart rate of a healthy lion is approximately normally distributed with mean
 =40 beats per minutes. ( Source The Merck Veterinary Manual) A heart rate
that is too slow or too fast can indicate a health problem. A veterinarian has
removed an abscessed tooth from a young, healthy zoo lion. As the animal slowly
starts to come out of the anesthetic, its heart rate (in beats per minute) is taken and
recorded for half an hour. Six samples were taken and its mean is 36.5 beats per
minute and sample standard deviation is 4.2. Use a 5% level of significance to test
the claim that the population average heart rate of the lion is different (either way)
from 40 beats per minute.
Ans. This is a t-test since we do not know the population standard deviation
and the sample size is less than 30. H 0 :   40; H1: :   40 It is a two-tail test
with critical values of -2.571 and 2.571. The degrees of freedom is 5. The test
value is -2.04. Since the test value falls is the acceptance region, we fail to
reject the null hypothesis.
3. The U.S. Department of Transportation reported hat 77% of all fatally injured
automobile drivers were intoxicated. A random sample of 36 records of
automobile driver fatalities in Kit Carson County, Colorado, showed that 20
involved an intoxicated driver. Do these data indicate that the population
proportion of driver fatalities related to alcohol is less than 77% in Kit Carson
County? Use   0.01.
This is a z-test for proportion. H 0 : p  0.77; H1: : p  0.77 It is a left tail test
with a critical value of -2.33. The test value is -3.05 So there is enough
evidence to reject the null hypothesis.