1.
Prospective studies on
nutrition often require subjects to keep detailed daily dieary logs. In contrast, retrospective studies often rely
on recall. Which method (dietary logs or
retrospective recall) do you believe is more likely to achieve accurate
results? Explain your response.
2. We often have a
choice of whether to record a given variable on either a quantitative or a
categorical scale. How does one measure
age quantitatively? Provide an example
by which age can be measured categorically.
3.
Telephone surveys may use a
telephone directory to identify individuals for study.
Speculate on the type of
household that would be undercovered by using this sampling frame.
4.
Could the number ‘0000” appear
in a table of random digits? If so, how
likely is this?
5.
Body weights of 18 diabetics
expressed as a percentage of ideal (defined as body weight divided by ideal body
weight x 100) are listed: (107, 119,
99,114,120,104,88,114,124,116,101,121,152,100,125,114,95,117) . Construct a stem –andleaf plot of these data
and interpret your findings.
6.
Name three measures of central
location
7.
To assess the air quality in a
surgical suite, the presence of colonyforming spores per cubic meter of air is
measured on three successive days. The
results are as follows: {12, 24, 30}.
Calculate the mean and standard deviation for these data.
8. In a lottery
game, a person must select 5 numbers from a total of 40. Tracy has chosen 7, 8, 9, 10, 11. Jaime has chosen 39, 17, 37, 5, 28. Who has a greater chance of winning?
9.In a box, there are 8 orange, 7 blue, and 6 red balls. One ball is selected randomly. What is the probability that it is neither
orange nor red?
10. A is
a numerical quantity that takes on different values depending on chance. There are two types of random variables. form a countable set of possible values. form an unbroken continuum of possible
values.
Answer the following questions covering
materials from previous chapters in your textbook. Each question is worth 3.5
points.
1. A telephone survey
uses a random digit dialing machine to call subjects. The random digit dialing
machine is expected to reach a live person 15% of the time. In eight attempts, what is the probability of achieving
exactly two successful calls?
2.
The
prevalence of a trait is 76.8%.
a.
In
a simple random sample of n = 5, how many individuals are
expected to exhibit this
b.
How
many would you expect to see with this characteristic in a simple random sample
of n
= 10?
c.
What
is the probability of seeing nine or more individuals with this characteristic
in a simple random sample of n = 10?
3. Linda hears a story on
National Public Radio stating that one in six eggs in the United States are
contaminated with Salmonella. If Salmonella contamination occurs
independently within and between egg cartons and Linda makes a three egg
omelet, what is the probability that her omelet will contain at least one Salmonella contaminated egg?
4. Suppose that heights
of 10year old boys vary according to a Normal distribution with µ = 138 cm and
? = 7 cm.
a.
What
proportion of this population is less than 150 cm tall?
b.
What
proportion is less than 140 cm in height?
c.
What
proportion is between 150 and 140 cm?
5. The Wechsler Adult
Intelligence Scale scores are calibrated to vary according to a normal
distribution with µ = 100 and ? = 15. What Wechsler scores cover the middle 50%
of the population? In other words, identify the 25^{th} percentile and
75^{th} percentile of the population.
Calculating percentile: 25th
6. Suppose that scores on
the biological sciences section of the Medical College Admissions Test (MCAT)
are normally distributed with a mean of 9.2 and a standard deviation of 2.2. Successful
applicants to become medical students had a mean score of 10.8 on this portion
of the test. What percentage of applicants had a score of 10.8 or greater?
7. A survey selects a
simple random sample of n = 500
people from a town of 55,000. The sample shows a mean of 2.30 health problems
per person (standard deviation = 1.65). Based on this information, say whether
each of the following statements is true
or false. Explain your reasoning in
each instance.
n = 500
a.
The
standard deviation of the sample mean is 0.074.
SE _{x?} = _?_
?n
b.
It
is reasonable to assume that the number of health problems per person will vary
according to a normal distribution.
c.
It
is reasonable to assume that the sampling distribution of the mean will vary
according to a normal distribution.
8. Ten people are given a
choice of two treatments. Let p
represent the proportion of patients in the patient population who prefer
treatment A. Among the 10 patients asked, 7 preferred method A. Assuming there
is no preference in the patient population (i.e., p = 0.5), calculate P(X >
7).
9. A simple random sample
of 18 male students at a university has an average height of 70 inches. The
average height of men in the general population is 69 inches. Assume that male
height is approximately normally distributed with ? = 2.8 inches. Conduct a
twosided hypothesis test to determine whether the male students are
significantly taller than expected. Show all hypothesis testing steps.
10. True or false? The pvalue refers to the probability of the
data or data more extreme assuming the null hypothesis.
Answer the following questions covering
materials from previous chapters in your textbook. Each question is worth 3.5
points.
1. A
sample of 49 sudden infant death syndrome (SIDS) cases had a mean birth weight
of 2998 g. Based on other births in the county, we will assume ? = 800 g. Calculate
the 95% confidence interval for the mean birth weight of SIDS cases in the
county. Interpret your results.
2.
A vaccine manufacturer analyzes a batch
of product to check its titer. Immunologic analyses are imperfect, and repeated
measurements on the same batch are expected to yield slightly different titers.
Assume titer measurements vary according to a normal distribution with mean µ
and ? = 0.070. Three measurements demonstrate titers of 7.40, 7.36 and 7.45. Calculate
a 95% confidence interval for true concentration of the sample.
3.
True or false? A confidence interval for
µ is 13 + 5.
4.
The term critical value is often used to refer to the value of a test
statistic that determines statistical significance at some fixed ? level for a
test. For example, +1.96 are the critical values for a twotailed ztest at ? = 0.05. In performing a ttest based on 21 observations, what
are the critical values for a onetailed test when ? = 0.05? That is, what
values of the t_{stat} will
give a onesided pvalue that is less
than or equal to 0.05? What are the critical values for a twotailed test at ?
= 0.05?
5.
When do you use a tprocedure instead of a zprocedure
to help infer a mean?
6.
A simple random sample of n = 26 boys between the ages of 13 and
14 has a mean height of 63.8 inches with a standard deviation 3.1 inches. Calculate
a 95% confidence interval for the mean height of the population.
7.
Identify whether the studies described
here are based on (1) single samples, (2) paired samples, or (3) independent
samples.
a. An
investigator compares vaccination histories in 30 autistic schoolchildren to a
simple random sample of nonautistic children from the same school district.
b. Cardiovascular
disease risk factors are compared in husbands and wives.
c. A
nutritional exam in applied to a random sample of individuals. Results are
compared to expected means and proportions.
8.
We wish to detect a mean difference of
0.25 for a variable that has a standard deviation of 0.67. How large a sample
is needed to detect the mean differences with 90% power at ? = 0.05
(twosided)?
9.
Identify two graphical methods that can
be used to compare quantitative data from two independent groups.
10. A
questionnaire measures an index of risktaking behavior in respondents. Scores
are standardized so that 100 represents the population average. The
questionnaire is applied to a sample of teenage boys and girls. The data for
boys is {72, 73, 86, 95, 95, 95, 96, 97, 99, 125}. The data for girls is {89,
92, 93, 98, 105, 106, 110, 126, 127, 130}. Explore the group differences with
sidebyside boxplots.
Answer the following questions covering materials from
previous chapters in your textbook. Each question is worth 7 points.
1.
A trial evaluated the feverinducing effects of three
substances. Study subjects were adults seen in an emergency room with diagnoses
of the flu and body temperatures between 100.0 and 100.9ºF. The three
treatments (aspirin, ibuprofen and acetaminophen) were assigned randomly to
study subjects. Body temperatures were reevaluated 2 hours after administration
of treatments. The below table lists the data.
Table: Decreases in body
temperature (degrees Fahrenheit)
Group 1 (aspirin) 
0.95 
1.48 
1.33 
1.28 

Group 2 (ibuprofen) 
0.39 
0.44 
1.31 
2.48 
1.39 

Group 3 (acetaminophen) 
0.19 
1.02 
0.07 
0.01 
0.62 
0.39 
Complete
an ANOVA for the above. What do you conclude?
2.
Evidence of nonrandom differences in group means occurs when
the variance between groups is __________ the variance within groups.
3. Why are scatterplots
necessary when investigating the relationship between quantitative variables?
4. r is always greater than or equal to _____ and less than or
equal to _____. Perfect negative association is present when r = _____. Perfect positive association
is present when r = _____. Between r = 0.56 and r = +0.46, the stronger correlation is _____.
5. Besides linearity,
what conditions are needed to infer population slope ? (3 more conditions)? Besides
linearity, what conditions are needed to infer population correlation coefficient
? (2 more conditions)?