April 24 Class Activity Solutions
1. A production line produces rulers that are supposed to be 12 inches long. A
sample of 49 of the rulers had a mean of 12.1 and a standard deviation of 0.5 inches.
The quality control specialist responsible for the production line decides to do a
hypothesis test at the 10% significance level to determine whether the production
line is really producing rulers that are 12 inches long or not.
a)
H 0 : µ=12
H a :   12
b) test statistic: z = 1.4
c) P-value: 0.1615
d) Conclusion: Do Not Reject the Null Hypothesis. The test is not significant.
e) Interpretation: We cannot conclude that the mean length of the rulers from the
production line in not equal to 12. We have not found the evidence to say the mean
length of the rulers is not 12. We should continue with our assumption that the
mean length of the rulers is 12.
2. A sample of 20 MSU freshmen had a mean GPA of 2.8 and a variance of 0.25
over all their courses taken in their first semester at MSU. Is the first semester GPA
of all MSU freshmen less than a B (3.0)? Perform a hypothesis test at 5%
significance level to answer this question
a) H 0 : µ = 3
Ha :   3
b) test statistic: t = = -1.79
c) P-value: 0.447
d) Conclusion: Reject the Null Hypothesis. The test is significant.
e) Interpretation: There is evidence that first semester mean freshman GPA at MSU
is lower than 3.0.
3. Suppose that an automobile manufacturer advertises that its new hybrid car has a
mean gas mileage of at least 50 miles per gallon. You take a simple random sample of n
= 30 hybrid vehicles and test their gas mileage. You find that in this sample, the
average is x̄ = 47 miles per gallon with a standard deviation of s = 5.5 miles per
gallon. Does this indicate that the advertiser’s statement is false?
a) H 0 : µ  50
H a :   50
b) test statistic: z = -2.98758
c) P-value: 0.0014
d) Conclusion: Reject the Null Hypothesis. The test is significant.
e) Interpretation: There is evidence to doubt the manufacturer’s claim. The average
gas mileage of these cars is less than 50 miles per gallon.
4. An industrial company claims that the mean pH level of the water in a nearby
river is 6.8. You randomly select 19 water samples and measure their pH. The mean
and standard deviation are 6.7 and 0.24, respectively. Is there enough evidence to
reject the company's claim at a 1% significance level? Assume the population is
normally distributed.
a) H 0 : µ=6.8
H a :   6.8
b) test statistic: t = -1.81621
c) P-value: 0.086
d) Conclusion: Do Not Reject the Null Hypothesis. The test is not significant.
e) Interpretation: : We cannot conclude that the mean pH level of the water in a
nearby river is not equal to 6.8. We should continue with our assumption that the
mean length of the rulers is 12.
5. The Internal Revenue Service claims that the mean wait time for callers
during a recent tax filing season was at most 7 minutes. A random sample of 11
callers has a mean wait time of 8.7 minutes and a standard deviation of 2.7
minutes. Is there enough evidence to reject the claim at a significance level of
0.10?
a) H 0 : µ  7
Ha :   7
b) test statistic: t = 2.088
c) P-value: 0.0316
d) Conclusion: Reject the Null Hypothesis. The test is significant.
e) Interpretation: There is evidence to believe that the mean waiting time is
greater than 7 minutes.
6. A used car dealer says that the mean price of a 2008 Honda CR-V is at least
$20,500. You suspect this claim is incorrect and find that a random sample of 14
similar vehicles has a mean price of $19,850 and a standard deviation of $1084. Is
there enough evidence to reject the dealer's claim at α = 0:05? Assume the
population of used car selling prices is approximately symmetric.
a) H 0 : µ  $20,500
H a :   $20,500
b) test statistic: z = -2.24361
c) P-value: 0.0124 (if you use the t-test, then the p-value is 0.02144)
d) Conclusion: Reject the Null Hypothesis. The test is significant.
e) Interpretation: There is evidence that the mean price of 2008 Honds CR-V is
less than $20,500.
7. The EPA reports that the exhaust emissions for a certain car model has a normal
distribution with a mean μ of 1.45 grams of nitrous oxide per mile and a standard
deviation σ of 0.4. The car manufacturer claims their new process reduces the
mean level of exhaust emitted for this car model. A simple random sample of 38
cars is taken and the mean level of exhaust emitted for this sample is 1.21 grams.
a) H 0 : µ = 1.45
H a :   1.45
b) test statistic: z = -3.698
c) P-value: 0.00009
d) Conclusion: : Reject the Null Hypothesis. The test is significant.
e) Interpretation: : There is evidence that the new process reduces the mean level
of exhaust below 1.45.