Hypothesis Testing Examples
1. A research meteorologist has been studying wind patterns over the Pacific Ocean. Based on these
studies, a new route is proposed for commercial airlines going from San Francisco to Honolulu. The new
route is intended to reduce flying time by taking advantage of existing wind patterns. It is known that for
the old route, the distribution of flying times for a large, four-engine jet has a mean of µ = 5.25 hrs with a
standard deviation of 0.6 hours. What null and alternative hypotheses should you use in order to
determine if the new route has decreased the average flying time?
2. Last year, your company’s service technicians took an average of 2.6 hours to respond to trouble calls
from business customers who had purchased service contracts. What null and alternative hypotheses
should you test in order to answer the question, “Does this year’s data show a significantly different
average response time?”
3. The Wall Street Journal reported that the average assembly time for the Ford Taurus is µ = 38 hours. A
modification to the assembly procedure has been made. It is thought that the average assembly time may
be reduced because of this modification. A random sample of 47 new Ford Taurus automobiles coming
off the assembly line showed the average assembly time to be x = 37.5 hours. The population has a
standard deviation of 1.2 hours. Suppose we are interested in testing whether this indicates that the
average assembly time has been reduced. What null and alternative hypothesis should you use?
4. A tire company has found that the mean time required for a mechanic to replace a set of four tires is 18
minutes with a standard deviation of 2 minutes. The company wishes to determine if instituting a new
installation procedure will reduce the mean installation time. Suppose that you wish to carry out the
above hypothesis test on a random sample of 40 installations. This sample yielded a mean installation
time of 17.4 minutes. What hypotheses should be used?
5. What are possible Type I and Type II errors for the situation described in example 1?
6. An experiment is carried out to determine if the mean donation per contributor to a certain charity has
increased since a new public relations program went into effect.
a) What should the null hypothesis be?
b) What should the alternative hypothesis be?
c) Describe a possible Type I error for this situation.
d) Describe a possible Type II error for this situation.
7. Carry out the appropriate hypothesis test on example 3 using a 5% level of significance.
8. Carry out the appropriate hypothesis test on example 4 using α = .01.
9. A random sample of 68 adult coyotes in a region of northern Minnesota showed the average age to be
x = 2.05 years with a sample standard deviation of 0.82 years. However, the overall population mean
age of adult coyotes is 1.75 years.
a) Carry out the appropriate hypothesis test to determine if the sample data indicates that coyotes in this
region of northern Minnesota tend to live longer than the average adult coyote. Use α = .01.
b) Would your critical value(s) change if you used a sample of size 20 instead? Why or why not?
If yes, what is(are) the new critical value(s)?
10. Last year, the mean number of books borrowed per cardholder at a major university was 18.5 books per
semester. A random sample of 100 cardholders showed the following results for this semester:
x = 19.54 books with a sample standard deviation of 6.31 books. The library administration would like
to know whether this semester’s mean usage has changed from last semester’s. Use α = .05.
11. Suppose you think that the proportion of people who wear contact lenses that experience no difficulty is
less than .80. You wish to conduct a hypothesis test to determine if you are correct.
a) Carry out the appropriate hypothesis test, assuming your sample is 200 students and that you find 149
of the people surveyed have experienced no difficulty. Use a 5% level of significance.
b) Carefully explain what the p-value means in this particular situation.
c) Is the result in part (a) statistically significant at the 5% level? At the 1% level?
12. Suppose we wish to compare the average lifetimes of Duracell Alkaline AA batteries to Eveready
Energizer Alkaline AA batteries. Suppose we take two independent samples of size 100 and get that
x 1 = 4.1 hours, 12 = 3.24; x 2 = 4.5 hours,  22 = 4 (where population 1 is Duracell). Carry out the
appropriate hypothesis test to determine if the average lifetime of Eveready Alkaline AA batteries is
different than that of Duracell batteries. Be sure to include the critical value(s) and the p-value. Use a
5% level of significance.
13. Let p1 denote the proportion of people who were unemployed in March, and let p2 denote the proportion
of people who were unemployed in April. Suppose that during late March, the government instituted
policies designed to lower the unemployment rate. We want to test whether the policies were effective.
In March, in a random sample of 1,000 people, 75 were unemployed. During April, in an independent
random sample of 1,000 people, 65 were unemployed. Carry out the appropriate hypothesis test using a
1% level of significance. Be sure you include the critical value(s) and the p-value.