Hypothesis Tests About a Population Mean, Exercises
In the following hypothesis tests, be sure to include all steps.
Example 1:
A student group maintains that the average student must travel for at least 25 minutes in
order to reach college each day. The college admissions office obtained a random sample of 31
one-way travel times from students. The sample had a mean of 19.4 min. and a standard deviation
of 9.6 min. Does the admissions office have sufficient evidence to reject the students’ claim? Use
the 𝛼 = 0.01 level of significance.
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Example 2:
Delco Products, a division of General Motors, produces commutators used in the electrical
systems of automobiles. The commutators are designed to be 18.810 mm in overall length. The
following random sample of 35 commutator lengths was taken while monitoring the manufacturing
process (all data values are in millimeters):
18.802
18.810
18.780
18.757
18.824
18.827
18.825
18.809
18.794
18.787
18.844
18.824
18.829
18.817
18.785
18.747
18.802
18.825
18.810
18.802
18.780
18.830
18.874
18.836
18.758
18.813
18.844
18.861
18.824
18.835
18.794
18.853
18.823
18.863
18.808
Is there sufficient evidence to reject the claim that these parts meet the design requirement “mean
length is 18.810 mm?” Use the 𝛼 = 0.01 level of significance.
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Example 3:
Selasphorus platycerus is the scientific name of the broad-tailed hummingbird that is
commonly found throughout the western United States. It is known that the mean incubation time
for eggs of this bird is approximately 16.5 days (based on information from The Hummingbird
Book, by D. Stokes and L. Stokes, Little, Brown and Company). Assume that incubation times are
approximately normally distributed. It is suspected that at higher elevations (above 8000 feet), the
mean incubation time might be different from 16.5 days. A number of broad-tailed hummingbird
nests were located in mountain country above 8000 feet, and incubation times for 18 eggs gave the
following information (in days):
15
19
16
16
18
17
21
18
17
16
17
18
19
16
15
21
23
19
Does this information provide sufficient evidence to conclude that the average incubation time for
broad-tailed hummingbird eggs at elevations above 8000 feet differs from 16.5 days? Use the α =
0.05 level of significance.
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Example 4:
A company that manufactures school supplies says that teachers spend a mean of more than
$580 of their own money on school supplies in a year. A random sample of the amounts (in dollars)
that 24 teachers spent on school supplies in a recent year is listed below.
523 581
476
600
721
622
575
320
888
875
910
643
596 587
398
622
585
700
590
710
729
857
630
520
Does this information provide sufficient evidence to support the company’s claim? Use the
α = 0.05 level of significance.
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Example 5:
An environmentalist estimates that the mean waste recycled by adults in the United States is
more than 1 pound per person per day. You want to test the claim. You find that the mean wasted
recycled per person per day for a random sample of 12 adults in the United States is 1.2 pounds and
the standard deviation is 0.3 pound. Does this information provide sufficient evidence to support
the environmentalist’s claim? Use the α = 0.05 level of significance.
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Example 6:
Consumer Reports indicated that the mean acceleration time (0 to 60 miles per hour) for the
Dodge Intrepid was 10.2 seconds. In most tests of this type, regular unleaded gasoline is used.
Suppose that 41 such tests were made using premium unleaded gasoline (octane over 91), and that
the sample mean accelerating time (0 to 6 mph) was found to be 𝑥̅ = 9.7 𝑠𝑒𝑐𝑜𝑛𝑑𝑠, with a sample
standard deviation of s = 2.1 seconds. Does this indicate that premium gasoline tends to reduce
average acceleration time (0 to 60 mph)? Use α = 0.05.
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