For each problem, select the best response.
(a) An engineer designs an improved light bulb. The previous design had an
average lifetime of 1200 hours. The new bulb had a lifetime of 1200.2 hours,
using a sample of 40,000 bulbs. Although the difference is quite small, the
effect was statistically significant. The explanation is
(b) Does 30 minutes of aerobic exercise each day provide significant
improvement in mental performance? To investigate this issue, a researcher
conducted a study with 150 adult subjects who performed aerobic exercise each day
for a period of six months. At the end of the study, 200 variables related to
the mental performance of the subjects were measured on each subject and the
means compared to known means for these variables in the population of all
adults. Nine of these variables were significantly better (in the sense of
statistical significance) at the level for the group that
performed 30 minutes of aerobic exercise each day as compared to the population
as a whole, and one variable was significantly better at the
level for the group that performed 30 minutes of aerobic exercise each day as
compared to the population as a whole. It would be correct to conclude
(c) The nicotine content in cigarettes of a certain brand is normally
distributed with mean (in milligrams) and standard deviation
. The brand advertises that the mean nicotine content of their
cigarettes is 1.5, but you believe that the mean nicotine content is actually
higher than advertised. To explore this, you test the hypotheses
, and you obtain a P-value of 0.052.
Which of the following is true?
You can earn partial credit on this problem.