Download What Test Should I Use?

Chapters 12 & 13
What Procedure Should I Use?
Name ___________________________
For each of the scenarios given, state the appropriate procedure
to use and why. Then write the appropriate hypotheses. Don't worry about necessary conditions for
these problems.
1. A study in the Journal of Psychology & Marketing(1992) investigates the degree to which American
consumers are concerned about product tampering. Large random samples of male and female
consumers were asked to rate their concerns about product tampering on a scale of 1 (little or no
concern) to 9 (very concerned.) What is the appropriate procedure to use to determine whether a
difference exists in the mean level of concern about product tampering between men and women?
The appropriate procedure to use is:
The appropriate hypothesis statement is
Ho :
because
Ha :
2. The Vividness of Visual Imagery Questionnaire (VVIQ) is widely used by behaviorists to assess
visual imagery. Scores range from 16 to 80, with a lower score representing greater vividness. A
group of St. Louis University researchers administered the VVIQ to a sample of 51 college students
on varsity sports teams. The mean and standard deviation of the VVIQ scores were 65.60 and 19.38,
respectively. In the general population, the mean VVIQ score is 67. What is the appropriate
procedure to use to determine whether the mean VVIQ score of college athletes is less than 67?
The appropriate procedure to use is:
The appropriate hypothesis statement is
Ho :
because
Ha :
3. Pond's Age-Defying Complex, a cream with alpha-hydroxy acid, advertises that it can reduce
wrinkles and improve the skin. In a study published in Archives of Dermatology (1996), 33 women
over the age of 40 used a cream with alpha-hydroxy for 22 weeks. At the end of the study period, 23
of the women exhibited skin improvement, as judged by a dermatologist. What is the appropriate test
to use to determine if the cream improves the skin of more than 60% of women over age 40?
The appropriate procedure to use is:
The appropriate hypothesis statement is
Ho :
because
Ha :
4. On average, do males outperform females in mathematics? To answer this question, psychologists at
the University of Minnesota compared the scores of male and female eighth-grade students who took
a basic skills mathematics achievement test (American Educational Research Journal, 1998). One
form of the test consisted of 68 multiple-choice
questions. A summary of the test scores is shown in
the table. What is the appropriate procedure to use to
determine if the true mean mathematics test scores of
female eighth-graders is higher than for males?
The appropriate procedure to use is:
The appropriate hypothesis statement is
Ho :
because
Ha :
5. Golf-course designers are concerned that old courses are becoming obsolete because new equipment
enables golfers to hit the ball so far. In effect, golf courses are "shrinking." One designer believes
that new courses need to be built with the expectation that players will be able to hit the ball more
than 250 yards (with their drivers), on average. Suppose a sample of 135 is tested, and their mean
distance is 256.3 yards with a standard deviation of 43.4 yards. What would be the appropriate
procedure to use to determine if the designer is correct about the average golfer?
The appropriate procedure to use is:
The appropriate hypothesis statement is
Ho :
because
Ha :
6. The Journal of Fish Biology (Aug. 1990) reported on a study to compare the incidence of parasites
(tapeworms) in species of Mediterranean and Atlantic fish. In the Mediterranean Sea, 588 brill were
captured and examined. 211 were found to be infected by the parasite. In the Atlantic Ocean, 123
brill were captured and examined and 26 were found to be infected. What would be the appropriate
procedure to use to determine if the proportion of brill infected with this parasite is different,
depending upon where the fish live?
The appropriate procedure to use is:
The appropriate hypothesis statement is
Ho :
because
Ha :
7. A group of University of Florida psychologists investigated the effects of age and gender on the
short-term memory of adults (Cognitive Aging Conference, Apr. 1996). Each in a sample of 152
adults was asked to place 20 common household items (e.g., eyeglasses, keys, hat, hammer) into the
rooms of a computer-image house. After performing some unrelated activities, each subject was
asked to recall the locations of the objects they had places. The number of correct responses (out of
20) was recorded. What would be the appropriate procedure to use to determine if women have a
higher mean recall score than men?
The appropriate procedure to use is:
The appropriate hypothesis statement is
Ho :
because
Ha :
8. A study reported in the Journal of Psychology (Mar. 1991) measures the change in female students'
self-concepts as they move from high school to college. A sample of 133 Boston College first-year
female students were selected for the study. Each was asked to rate several aspects of her life at two
points in time: at the end of her senior year of high school, and during her sophomore year of college.
What would be the appropriate procedure to use to determine whether the mean self-concept of
females decreases between the senior year of high school and sophomore year of college?
The appropriate procedure to use is:
The appropriate hypothesis statement is
Ho :
because
Ha :
9. A consumer protection group is concerned that a ketchup manufacturer is filling its 20-ounce familysize containers with less than 20 ounces of ketchup. The group purchases 30 family-size bottles of
this ketchup, weighs the contents of each, and finds that the mean weight is equal to 19.86 ounces,
and the standard deviation is equal to .22 ounce. What would be the appropriate procedure to use to
determine if the company is under-filling its ketchup containers?
The appropriate procedure to use is:
The appropriate hypothesis statement is
Ho :
because
Ha :
These problems are all from Statistics: eighth edition, by McClave & Sincich. Prentice Hall, 2000.
Answers:
1. 2 sample t-test because data are from 2
samples from 2 independent populations.
2. t-test because there is one sample and
sigma is unknown
H o : µm = µ f
H o : µ = 67
H a : µm ! µ f
H a : µ < 67
m = male; f = female
3. 1-proportion z-test because there is one
sample and the parameter of interest is a
proportion.
H o : p = 0.60
H a : p > 0.60
4. 2 sample t-test because there are 2
samples from 2 independent populations.
H o : µm = µ f
H a : µm < µ f
m = male; f = female
5. t-test because there is one large sample
and sigma is unknown
H o : µ = 250 yards
H a : µ > 250 yards
6. 2-proportion z-test because there are 2
samples from 2 independent populations
and the parameters of interest are
proportions.
H o : pA = pM
H a : pA ! pM
A = Atlantic fish: M = Mediterranean fish
7. 2 sample t-test because data are from 2
samples from 2 independent populations.
H o : µw = µ m
H a : µw > µ m
w = women; m = men
8. paired t-test because each student is
paired with herself and the parameter of
interest is the mean difference in self-image
scores at two different points in time.
H o : µ diff = 0
H a : µ diff > 0
diff = score at end of high school – score in
sophomore year of college
9. t-test for means because there is one sample and sigma is unknown
H o : µ = 20 ounces
H a : µ < 20 ounces