AP Statistics
Ch. 21 Class notes
What’s a “Type I error”? …a “Type II error”?
What’s an “alpha level”?
p. 499, #5 Alpha Levels A researcher developing scanners to search for hidden weapons at
airports has concluded that a new device is significantly better than the current scanner. He
made this decision based on a test using  = .05 . Would he have made the same decision at
 = .10 ? How about  = .01 ? Explain.
Med School According to the Association of American Medical Colleges, only 46% of medical
school applicants were admitted to a medical school in the fall of 2006. Upon hearing this, the
trustees of Striving College expressed concern that only 77 out of 180 students in their class of
2006 who applied to medical school were admitted, The college president assured the trustees
that this was just the kind of year-to year fluctuation in fortunes that is to be expected and that,
in fact, the school’s success rate was consistent with the national average.
We perform a one-tail lower tail hypothesis test and get a p-value of 0.19, which is not that
unusual a result. It may just be year-to –year fluctuation, as the president says.
If we made a mistake, and failed to reject Ho when Ho is false, we have committed a
Type II error. Explain in context what this means. What might be the consequences of
making such and error?
Football 2006 During the 2006 season, the home team won 136 of the 240 regular-season National
Football League games, Is this strong evidence of a home field advantage in professional football?
We perform a one-tailed upper tail test and get a p-value of .02, which leads us to reject Ho.
Evidence suggests that there is a home field advantage in professional football.
If we made a mistake, and rejected Ho when Ho is true, we have committed a Type I error.
Explain in context what this means. What might be the consequences of making such an
error?
Sensor: A company claims to have invented a hand-held sensor that can detect the presence of
explosives inside a closed container. Law enforcement and security agencies are very interested
in purchasing several of the devices if they are shown to perform effectively. An independent
laboratory arranged a preliminary test. If the device can detect explosives at a rate greater than
chance would predict, a more rigorous test will be performed. They placed four empty boxes in
the corners of an otherwise empty room. For each trial they put a small quantity of an explosive
in one of the boxes selected at random. The company’s technician then entered the room and
used the sensor to try to determine which of the four boxes contained the explosive. The
experiment consisted of 50 trials, and the technician was successful in finding the explosive 16
times.
a) Does this indicate that the device is effective in sensing the presence of explosives, and
should undergo more rigorous testing?
b) What does the p-value mean in this context?
c) If we made an error, what type of error did we make? Describe in context.
d) What could the company do to reduce the chance of putting their faith in a bogus sensor
(Type I error)?
Toothpaste: The board of directors for Procter and Gamble is concerned that only 19.5% of the
people who use toothpaste buy Crest toothpaste. A marketing director suggests that the
company invest in a new marketing campaign which will include new labeling for the
toothpaste. The research department conducts product trials in test markets for one month to
determine if the market share increases with new labels.
a) In this context describe a Type I error and the impact such an error would have on the
company.
b) In this context describe a Type II error and the impact such an error would have on the
company.
c) What is the power of the test in this situation? What could the company do to increase
the power of the test, now that the data has already been collected (that is, they cannot
increase the sample size)?
d) (Review) Based on the data they collected during the trial the research department
found that a 98% confidence interval for the proportion of all consumers who might buy
Crest toothpaste was (16%, 28%). What conclusion should the company reach about the
new marketing campaign? Explain.