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Chapter 10.2 – TESTS OF SIGNIFICANCE
Confidence Intervals – goal is to estimate a population parameter from your sample
Tests of Significance – goal is to assess the evidence provided by data about some claim concerning a
population parameter: something changing or if working properly
AN OUTCOME THAT WOULD RARELY HAPPEN IF A PARAMETER WERE TRUE
IS GOOD EVIDENCE THAT THE PARAMETER HAS CHANGED
1. STUDENT ATTITUDES. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that
measures the attitudes toward school and study habits of students. Scores range from 0 to 200 and
are normally distributed. The mean score for US college students is about 115, with a standard
deviation of 30. A teacher suspects that older students have better attitudes toward school. She
gives the SSHA to 25 students who are at least 30 years of age.
(a) State all the information
(b) State the null and alternative hypothesis
(c) Suppose that the sample data gave x = 118.6, and another gave x = 125.7. Is one result
better evidence that the mean score of all older students is greater than 115 and the other
outcome not?
(d) Test the data.
(e) Give the appropriate conclusion
2. The cost of good running shoes has gone up over the years but companies are now trying to make
them more affordable for runners. A researcher claims that the average cost of men’s athletic shoes
is less than $100. He selects a random sample of 36 pairs of shoes from a catalog and finds the
following costs:
80
90
95
75 100 75
70
60 100 90
70 115
140 110 95 105 100 80 130 85 100 105 105 65
95
80 110 110 80 115 130 105 65 110 90
90
Test the researchers claim. (It is known that the cost of athletic shoes are normally distributed with
a standard deviation of $18).
3. The average “moviegoer” sees 8.5 movies a year with a standard deviation of 3.2 movies. A large
university claims that the average number of movies that their students see a year is different than
the national average. A random sample of 40 moviegoers from this university revealed that the
average number of movies seen per person was 9.4. Test the University’s claim.
4. Radon is a colorless, odorless gas that is naturally released by rocks and soils and may concentrate
in tightly closed houses. Because radon is slightly radioactive, there is some concern that it may be
a health hazard. Radon detectors are sold to homeowners worried about risk, but the detectors may
be inaccurate. University researchers placed 12 detectors in a chamber where they were exposed to
105 picocuries per liter of radon over 3 days. Here are the readings given by the detectors (σ = 9):
91.9 97.8 111.4 122.3 105.4 95.0 103.8 99.6 96.6 119.3 104.8 101.7
(a) Give a 90% confidence interval for the mean reading for this type of detector and interpret it.
(b) Is there significant evidence at the 10% level that the mean reading differs from the true value
of 105?
2006 AP STATISTICS FREE-RESPONE QUESTION (FORM B) #3
Golf balls must meet a set of five standards in order to be used in professional tournaments. One of
these standards is distance traveled. When a ball is hit by a mechanical device, Iron Byron, with a
10-degree angle of launch, a backspin of 42 revolutions per second, and a ball velocity of 235 feet
per second, the distance the ball travels may not exceed 291.2 yards. Manufacturers want to
develop balls that will travel as close to the 291.2 yards as possible without exceeding that distance.
A particular manufacturer has determined that the distances traveled for the balls it produces are
normally distributed with a standard deviation of 2.8 yards. This manufacturer has a new process
that allows it to set the mean distance the ball will travel.
(a) If the manufacturer sets the mean distance traveled to be equal to 288 yards, what is the
probability that a ball that is randomly selected for testing will travel too far?
(b) Assume the mean distance traveled is 288 yards and that five balls are independently tested.
What is the probability that at least one of the five balls will exceed the maximum distance of
291.2 yards?
(c) If the manufacturer wants to be 99 percent certain that a randomly selected ball will not exceed
the maximum distance of 291.2 yards, what is the largest mean that can be used in the
manufacturing process?