Practice Sheet – 1 Sample Tests
(1) According to the 1990 census, 19.9% of all households in Greensboro consisted of a
“married couple with children.” This year, a researcher took a random sample of 400
households in Greensboro and found that there were 90 households with a “married
couple with children.” Is there a significant difference between this year’s data and
the 1990 data? Test at the 1% level of significance.
(2) Suppose we want to investigate the claim that at least 75% of students attending a
university are opposed to a plan to increase student fees in order to build new parking
facilities. A sample survey reveals 201 of 300 students are opposed. Test the claim
at a 1% level of significance.
(3) The Acme Widget Company produces widgets with an average weight of 120 g. A
quality control technician takes a sample of 64 widgets and finds that the average
weight of widgets in the sample is 117 g with standard deviation of 3 g. Is the
difference significant? Test at the 1% level.
(4) A machine should be set to produce tubes with an average inside diameter of 1.40 cm.
A random sample of 10 tubes is taken and the sample has an average inside diameter
of 1.50 cm with a standard deviation of 0.15 cm. Is the machine set too high? Test at
the 5% level.
(5) A cigarette manufacturer claims its cigarettes have an average nicotine content of 18.3
mg. If a random sample of 7 cigarettes has nicotine contents of 20, 17, 21,19, 22, 21,
and 16 mg, would you agree with the claim? Test at the 5% level.
(6) A certain brand of tire is advertised to have a life of 50,000 miles. After a number of
complaints concerning excessive treadwear for the brand of tire, a consumer testing
group decides to test the company’s claim. They take a random sample of 10 tires
and find an average life of 47,000 miles with a SD of 7,500 miles. Can the consumer
testing group conclude that the company’s advertised claim is false? Test at the 1%
level.
Solution Key for 1 Sample Tests
(1) z  1.3  P  9.5%  there does not seem to be a significant difference between this
year’s data and the 1990 data.
(2) z  3.2  P  .07%  there seems to be significantly fewer than 75% of the
students who oppose the plan.
(3) z  8  P  0%  the difference seems to be significant.
(4) t  2  with df = 9, 2.5% < P < 5%  it seems that the machine is set too high.
(5) t  1.345  with df = 6, 10% < P < 25%  there does not seem to be evidence for
rejecting the claim.
(6) t  1.2  with df = 9, 10% < P < 25%  there is no evidence to conclude that the
claims are false.