Solutions to All Exercises 277
1.7
H0: The average tomato yield for Brand A fertilizer is the same as the average tomato yield for the more expensive
Brand B fertilizer.
H1: The average tomato yield for the more expensive Brand B fertilizer is greater than the average tomato yield for
the Brand A fertilizer.
Type I Error: Spend more money on the Brand B fertilizer when it really is not better than the Brand A fertilizer
regarding the average tomato yield. Type II Error: Continue to use the Brand A fertilizer when the Brand B
fertilizer results in a higher tomato yield on average.
1.8
(a) Type I error: to classify a person as a drug user when he/she is not. Type II error: to classify a person as a non-
drug user when he/she actually is.
(b) Since the test classifies the person as a drug user (i.e. rejects H0) 4% of the time when the person is not a drug
user (i.e. H0 is true), the chance of a Type I error is 4%.
1.9
A Type I error is rejecting the null hypothesis when it is true. So the owner would conclude the patrons are older
and the owner would spend the time and money to remodel, when the crowd is actually not older. The owner would
have spent money unnecessarily and the remodeling may not appeal to some of the patrons, but in general, it is not a
serious error.
1.10
Based on the article "U.S. Health Improves but Rural Areas Lag," from CNN, September 10, 2001. Summary of the
article appears below. Contains many possible hypotheses.
H0: People in Rural areas of the US are as healthy as their urban counterparts.
H1: People in Rural areas of the US are less healthy than their urban counterparts.
Type I error: conclude that rural people are less healthy than urban people when in fact they are not.
Type II error: conclude that rural people are as healthy as urban people when in fact it isn't the case.
Summary of article: " Americans overall are healthier today than they were 25 years ago. A new government report
offers some reasons: longer life expectancy, better infant survival, fewer smokers, less hypertension and lower
cholesterol levels. But in small-town America, the news on health is far from good, said an annual report released
Monday by the Centers for Disease Control and Prevention. Rural residents tend to smoke more, lose more teeth as
they age and die sooner than suburban and many big-city counterparts, the government snapshot of the country's
health shows. For instance: --10.6 percent of the wealthiest residents in rural areas and 10 percent of urban residents
lacked health insurance in 1997 and 1998, compared with about 6.6 percent of suburbanites. --37.6 percent of rural
residents over 65 had edentulism, a total loss of teeth, in 1997 and 1998, compared with about 25.7 percent in the
suburbs and 26.8 percent in cities. --18.9 percent of children age 12 to 17 in the most rural areas were regular
smokers in 1999, compared with 11 percent in urban areas and 15.9 percent in the suburbs. Rural adults also smoked
at higher rates than urban or suburban adults. --46.5 of men and women in the most rural areas did not exercise, play
sports or pursue active hobbies in 1997 and 1998, compared with 40.9 percent of urban dwellers and 31.1 percent of
