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Assignment #11
Inferences About Means and Proportions Using z tests
Use the Inferential Tests in Excel spreadsheet to answer these questions. You may also use a
graphing calculator such as a TI-83 if you prefer. You may work on solving these problems
together with your partner. Each of you should then complete an Inferential Statistics Answer
Sheet on four of these problems. Therefore, for the purposes of completing the answer sheets,
divide the problems between you and your partner, completing worksheets on different problems.
You may work together and have some discussion about each problem but each person should
turn in the numeric answers to all problems as well as a completed answer sheet on four of the
problems. Along with the numeric answers, mention the type of test you used to solve the
problem, and whether it was a one tailed or two tailed test. You may need to refer to the
textbook and the Decision Tree for some of the information required by the answer sheet.
11.1
Medical researchers know from many large nationally representative studies that the duration of a
bout with the common cold is normally distributed with a population mean of about 4 days and a
standard deviation of about 2 days. A researcher wants to test whether a new medication will
shorten the duration of a bout with the common cold. Subjects were randomly selected and then
randomly assigned to receive the new drug or a placebo and then were infected with the cold bug.
Using the following data, test whether it is reasonable to conclude that the drug is effective.
n
Mean Days Duration
SD
Drug Group
20
2.97
2.05
Placebo Group
20
4.14
1.95
11.2
A psychologist suspects that people who attend his workshops on cognitive behavior
modification are more depressed than the general population. He takes a random sample of
attendees to his workshops and administers a depression inventory to them. Given the following
information, can we reject Ho and conclude that the attendees are more depressed than the
national average? The sample of depression scores is distributed approximately normally and
higher scores indicate more depression.
Sample Depression Scores
Population Norm Depression Scores
Mean = 58.56
Mean=50
SD=10.79
SD=10
n=100
11.3
In a commentary on the educational level of the American workforce, a radio talk show host
made the claim, “The average young person in this country can’t even balance a checkbook.”
The National Assessment of Educational Progress (NAEP) says that a score of 275 or higher on
its quantitative test reflects the skill needed to balance a checkbook. The NAEP random sample
of 840 young people had a mean score of 272.69 (sample standard deviation=59.62), a bit below
the checkbook-balancing level. Is this sample result evidence enough to conclude that the mean
for all young people is less than 275 (population standard deviation=60)?
11.4
A survey was conducted using a random sample of undergraduate students from UNC Charlotte.
The study found that approximately 30% of the students report that they suffer from allergies.
The study contained 200 respondents. Assuming that the students who responded are similar to
the population of undergraduate students as a whole, conduct a test to determine if there is a
difference between students at UNC Charlotte and the national CDC statistics for the population
of undergraduate college students, which report that 34% report allergies.
11.5
The concentration of lead in the drinking water from 100 randomly sampled homes drawn in
each of two different sections of Charlotte revealed the following means (in parts per million or
ppm):
n
Mean
SD
Sample 1
100
34.11
5.97
Sample 2
100
36.03
6.02
We have reason to believe that the population standard deviation is 6 and that the data is
normally distributed. Conduct a statistical significance test to determine if there is a difference in
lead concentration between the two sections of the city.
11.6
Jobey Thomas made 44% of his three point attempts for his entire basketball career including his
first two years at UNC Charlotte. Over the summer, Coach Lutz detected a slight mechanical
flaw in his release and suggested a change to Jobey’s jump shot. During this season, his junior
year of Conference USA play, Jobey is 26 for 51 from behind the three-point line. Did Coach
Lutz make a difference in Jobey’s success in shooting three pointers?
11.7
An elementary Principal was charged by the Superintendent with the task of reporting on the
state of the quality of kindergartens in a large school system. She decided to have trained
observers collect Assessment Profile scores on a random sample of 30 classrooms from across
the district. Each Assessment Profile scale score is scaled to have a normal distribution and
national norms with a mean of 50 and a standard deviation of 10. The sample data for each scale
is distributed approximately normally. Given the data below, is she justified in concluding that
kindergarten classrooms in the system are different from the national average in quality for the
scale score listed below?
Learning Environment
11.8
mean=57.34
SD=9.89
A bag of M&Ms contains 10 red out of 58 total M&Ms. If the manufacturer assures us that
typical bags contain 27% M&Ms, did this bag come from the typical batch?
11.9
The Diana-Dusseldorf School System is interested in conducting a study to determine the effect
of the Pillow Talk Test Prep Kit. The kit consists of several magic bullets that are stored in a
small Ziploc bag and placed under a student’s pillow the night before an EIEIO test. One
hundred third grade students are selected at random from across the county. Fifty are randomly
assigned to the Pillow Talk group and fifty are assigned to the control group. All study children
are informed that a mock State EIEIO Test will be given in one week. The Pillow Talk children
are given the kits along with instructions for their parents regarding the proper methods of subpillow placement. The EIEIO test is scaled to have a normal population distribution, a
population mean of 50, and a population standard deviation of 10. Use the data below from the
practice test to conduct a statistical significance test to determine if the magic bullets are
effective.
Mean
SD
Treatment Group
Control Group
52.45
10.42
49.78
10.38
11.10
A high school Principal had just received the test scores of 100 seniors on the new achievement
test. The mean test score of the seniors was 106.78 and the standard deviation was 29.76. The
mean of the test scores for all students who took the test was 100 with a standard deviation of 30.
The principal was very proud. Was the principal justified? That is, did the seniors in her high
school score statistically significantly higher than the mean of all students who took the test?
11.11
A national politician made a speech in which he railed against the drinking habits of today’s
college students. He implied that the majority of undergraduate college students in America are
problem drinkers. You discover the 1995 Harvard School of Public Health College Alcohol
Study, which examined alcohol use among college students. The study asked students about
their drinking habits and then classified students as social drinkers, binge drinkers, and problem
drinkers based on their responses. Using a nationally representative, simple random sample of
17,592 college students, they reported the following results:
Respondents who reported the behaviors of social drinkers: 15,678
Respondents who reported the behaviors of binge drinkers: 7,741
Respondents who reported the behaviors of problem drinkers: 2,549
You find the following survey results from Queens College, using a sample of 150 of their
students:
Respondents who reported the behaviors of social drinkers: 137
Respondents who reported the behaviors of binge drinkers: 68
Respondents who reported the behaviors of problem drinkers: 11
Assume that the Harvard study, given its large nationally representative sample, is giving you the
true population percentages. Are Queens College students different from students nationally in
the social drinking category?
11.12
A study was undertaken to investigate whether it is more difficult for children with learning
disabilities (LD) to make friends if they are placed in a separate special class for LD children or
in an integrated classroom. LD children were randomly selected and then randomly assigned as
follows: 45 were placed in separate LD classes and 45 were placed in integrated classrooms. At
the end of 7 months, the number of friends made by each student was recorded with these results:
n
Mean
SD
Sample 1
45
5.09
2.92
Sample 2
45
5.32
2.89
We have reason to believe that the population standard deviation is 3 and that the data is
normally distributed. Conduct a statistical significance test to determine if there is a difference
between the two groups of children in their ability to make friends.