Solutions Manual Fundamentals of
Biostatistics 8th Edition Bernard Rosner
Section 1: Descriptive Statistics and Probability Distributions
hg hg hg hg hg hg
1. The median is preferred over the mean as a measure of central tendency when:
hg hg hg hg hg hg hg hg hg hg hg hg hg hg
A) The data are normally distributed
hg hg hg hg hg
B) The data contain outliers or are skewed
hg hg hg hg hg hg hg
C) The data are measured on a nominal scale
hg hg hg hg hg hg hg hg
D) The sample size is very large
hg hg hg hg hg hg
Answer: B – hg hg
The median is robust to outliers and skewed data, making it a better measure of central tende
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
ncy when these conditions exist .
hg hg hg hg hg
2. Which of the following statements about the standard normal distribution is FALSE?
hg hg hg hg hg hg hg hg hg hg hg hg
A) Its mean is 0
hg hg hg hg
B) Its variance is 1
hg hg hg hg
C) It is symmetric about 0
hg hg hg hg hg
D) Its support is from 0 to 1
hg hg hg hg hg hg hg
Answer: D – The standard normal (Z) distribution has infinite support from -
hg hg hg hg hg hg hg hg hg hg hg hg
∞ to +∞, not from 0 to 1 .
hg hg hg hg hg hg hg hg
3. The Z-score is calculated as:
hg hg hg hg hg
A) (observed value - mean) / variance
hg hg hg hg hg hg
B) (observed value - mean) / standard deviation
hg hg hg hg hg hg hg
C) (observed value - standard deviation) / mean
hg hg hg hg hg hg hg
D) (mean - observed value) / standard error
hg hg hg hg hg hg hg
Answer: B – Z = (observed value - hg hg hg hg hg hg hg
mean) / standard deviation. It measures how many standard deviations an observation is from
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
the mean . hg hg
4. For the binomial distribution, which condition makes the Poisson approximation most
hg hg hg hg hg hg hg hg hg hg hg h
appropriate?
g
,A) Large n and small p
hg hg hg hg hg
B) Small n and large p
hg hg hg hg hg
C) Large n and large p
hg hg hg hg hg
D) n and p are equal
hg hg hg hg hg
Answer: A – hg hg
The Poisson approximation to the binomial is appropriate when n is large and p is small (the r
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
are events condition) .
hg hg hg
5. Suppose the expected number of deaths due to bladder cancer over 20 years is 1.8, an
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
d 6 deaths are reported. Using the Poisson distribution, the probability of exactly 6 deat
hg hg hg hg hg hg hg hg hg hg hg hg hg hg
hs is: hg
A) 0.010
hg
B) 0.025
hg
C) 0.050
hg
D) 0.100 hg
Answer: A – Using the Poisson distribution with λ = 1.8, P(X = 6) is approximately 0.010 .
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
Section 2: Confidence Intervals and Hypothesis Testing
hg hg hg hg hg hg
6. A 99% confidence interval will be ______ than a 95% confidence interval for the same d
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
ata.
A) Narrower
hg
B) Wider
hg
C) The same width
hg hg hg
D) Impossible to determine
hg hg hg
Answer: B – hg hg
Higher confidence requires a larger multiplier (z or t), which widens the interval, providing gre
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
ater certainty but less precision .
hg hg hg hg hg
7. If a test has a p-value of 0.06 at α = 0.05, the correct decision is:
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
A) Reject H₀ and conclude significance
hg hg hg hg hg
B) Fail to reject H₀ and conclude no statistically significant effect
hg hg hg hg hg hg hg hg hg hg
C) Accept H₀ as true
hg hg hg hg
D) Recompute with a larger sample
hg hg hg hg hg
,Answer: B – hg hg
Since p > 0.05, we fail to reject the null hypothesis. However, we do not "accept" H₀ as true; w
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
e simply lack evidence to reject it .
hg hg hg hg hg hg hg
8. A Type I error is defined as:
hg hg hg hg hg hg hg
A) Failing to reject a false null hypothesis
hg hg hg hg hg hg hg
B) Rejecting a true null hypothesis
hg hg hg hg hg
C) Correctly rejecting a false null hypothesis
hg hg hg hg hg hg
D) Correctly not rejecting a true null hypothesis
hg hg hg hg hg hg hg
Answer: B – Type I error = false positive, with probability α (the significance level) .
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
9. A researcher plans to compare the means of two independent groups with sample size
hg hg hg hg hg hg hg hg hg hg hg hg hg hg
s of 30 each and normally distributed data. Which test is most appropriate?
hg hg hg hg hg hg hg hg hg hg hg hg
A) Paired t-test
hg hg
B) Independent samples t-test
hg hg hg
C) Mann-Whitney U test
hg hg hg
D) One-way ANOVA
hg hg
Answer: B – hg hg
For comparing means of two independent groups with normally distributed data, the indepen
hg hg hg hg hg hg hg hg hg hg hg hg hg
dent samples t-test is appropriate .
hg hg hg hg hg
10. The standard error (SE) differs from the standard deviation (SD) in that:
hg hg hg hg hg hg hg hg hg hg hg hg
A) SE is always larger than SD
hg hg hg hg hg hg
B) SE measures variability of sample means, while SD measures variability of individual observat
hg hg hg hg hg hg hg hg hg hg hg hg hg
ions
C) SE is used for descriptive statistics only
hg hg hg hg hg hg hg
D) SE does not depend on sample size
hg hg hg hg hg hg hg
Answer: B – hg hg
SE is the standard deviation of the sampling distribution of the mean, while SD measures varia
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
bility of individual observations. SE = SD/√n .
hg hg hg hg hg hg hg
Section 3: ANOVA and Regression hg hg hg hg
, 11. In a multiple regression model Y = β₀ + β₁X₁ + β₂X₂ + ε, the coefficient β₁ represents
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
:
A) The change in Y for a 1-unit change in X₁, holding X₂ constant
hg hg hg hg hg hg hg hg hg hg hg hg hg
B) The change in Y for a 1-unit change in X₁, ignoring X₂
hg hg hg hg hg hg hg hg hg hg hg hg
C) The intercept when X₁ = 0
hg hg hg hg hg hg
D) The change in Y for a 1-unit change in X₂
hg hg hg hg hg hg hg hg hg hg
Answer: A – hg hg
In multiple regression, β₁ is the partial regression coefficient representing the change in Y for a
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
1-unit change in X₁ while holding all other variables constant .
hg hg hg hg hg hg hg hg hg hg hg
12. The F-statistic in a one-way ANOVA is calculated as:
hg hg hg hg hg hg hg hg hg
A) MS(between) / MS(within)
hg hg hg
B) MS(within) / MS(between)
hg hg hg
C) SS(between) / SS(within)
hg hg hg
D) SS(total) / SS(between)
hg hg hg
Answer: A – hg hg
F = mean square between groups divided by mean square within (error). A large F suggests gr
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
oup means differ significantly .
hg hg hg hg
13. The degrees of freedom for the chi-
hg hg hg hg hg hg hg
square test of independence in a 3×4 contingency table are:
hg hg hg hg hg hg hg hg hg
A) 12hg
B) 11hg
C) 6 hg
D) 2 hg
Answer: C – df = (r-1)(c-1) = (3-1)(4-1) = 2 × 3 = 6 .
hg hg hg hg hg hg hg hg hg hg hg hg hg hg
14. In a scatterplot, if the points fall exactly on a straight line with a positive slope, the c
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
orrelation coefficient r equals: hg hg hg
A) 0 hg
B) -1hg
C) +1hg
D) 0.5hg
Answer: C – Perfect positive linear correlation yields r = +1.0 .
hg hg hg hg hg hg hg hg hg hg hg
Biostatistics 8th Edition Bernard Rosner
Section 1: Descriptive Statistics and Probability Distributions
hg hg hg hg hg hg
1. The median is preferred over the mean as a measure of central tendency when:
hg hg hg hg hg hg hg hg hg hg hg hg hg hg
A) The data are normally distributed
hg hg hg hg hg
B) The data contain outliers or are skewed
hg hg hg hg hg hg hg
C) The data are measured on a nominal scale
hg hg hg hg hg hg hg hg
D) The sample size is very large
hg hg hg hg hg hg
Answer: B – hg hg
The median is robust to outliers and skewed data, making it a better measure of central tende
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
ncy when these conditions exist .
hg hg hg hg hg
2. Which of the following statements about the standard normal distribution is FALSE?
hg hg hg hg hg hg hg hg hg hg hg hg
A) Its mean is 0
hg hg hg hg
B) Its variance is 1
hg hg hg hg
C) It is symmetric about 0
hg hg hg hg hg
D) Its support is from 0 to 1
hg hg hg hg hg hg hg
Answer: D – The standard normal (Z) distribution has infinite support from -
hg hg hg hg hg hg hg hg hg hg hg hg
∞ to +∞, not from 0 to 1 .
hg hg hg hg hg hg hg hg
3. The Z-score is calculated as:
hg hg hg hg hg
A) (observed value - mean) / variance
hg hg hg hg hg hg
B) (observed value - mean) / standard deviation
hg hg hg hg hg hg hg
C) (observed value - standard deviation) / mean
hg hg hg hg hg hg hg
D) (mean - observed value) / standard error
hg hg hg hg hg hg hg
Answer: B – Z = (observed value - hg hg hg hg hg hg hg
mean) / standard deviation. It measures how many standard deviations an observation is from
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
the mean . hg hg
4. For the binomial distribution, which condition makes the Poisson approximation most
hg hg hg hg hg hg hg hg hg hg hg h
appropriate?
g
,A) Large n and small p
hg hg hg hg hg
B) Small n and large p
hg hg hg hg hg
C) Large n and large p
hg hg hg hg hg
D) n and p are equal
hg hg hg hg hg
Answer: A – hg hg
The Poisson approximation to the binomial is appropriate when n is large and p is small (the r
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
are events condition) .
hg hg hg
5. Suppose the expected number of deaths due to bladder cancer over 20 years is 1.8, an
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
d 6 deaths are reported. Using the Poisson distribution, the probability of exactly 6 deat
hg hg hg hg hg hg hg hg hg hg hg hg hg hg
hs is: hg
A) 0.010
hg
B) 0.025
hg
C) 0.050
hg
D) 0.100 hg
Answer: A – Using the Poisson distribution with λ = 1.8, P(X = 6) is approximately 0.010 .
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
Section 2: Confidence Intervals and Hypothesis Testing
hg hg hg hg hg hg
6. A 99% confidence interval will be ______ than a 95% confidence interval for the same d
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
ata.
A) Narrower
hg
B) Wider
hg
C) The same width
hg hg hg
D) Impossible to determine
hg hg hg
Answer: B – hg hg
Higher confidence requires a larger multiplier (z or t), which widens the interval, providing gre
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
ater certainty but less precision .
hg hg hg hg hg
7. If a test has a p-value of 0.06 at α = 0.05, the correct decision is:
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
A) Reject H₀ and conclude significance
hg hg hg hg hg
B) Fail to reject H₀ and conclude no statistically significant effect
hg hg hg hg hg hg hg hg hg hg
C) Accept H₀ as true
hg hg hg hg
D) Recompute with a larger sample
hg hg hg hg hg
,Answer: B – hg hg
Since p > 0.05, we fail to reject the null hypothesis. However, we do not "accept" H₀ as true; w
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
e simply lack evidence to reject it .
hg hg hg hg hg hg hg
8. A Type I error is defined as:
hg hg hg hg hg hg hg
A) Failing to reject a false null hypothesis
hg hg hg hg hg hg hg
B) Rejecting a true null hypothesis
hg hg hg hg hg
C) Correctly rejecting a false null hypothesis
hg hg hg hg hg hg
D) Correctly not rejecting a true null hypothesis
hg hg hg hg hg hg hg
Answer: B – Type I error = false positive, with probability α (the significance level) .
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
9. A researcher plans to compare the means of two independent groups with sample size
hg hg hg hg hg hg hg hg hg hg hg hg hg hg
s of 30 each and normally distributed data. Which test is most appropriate?
hg hg hg hg hg hg hg hg hg hg hg hg
A) Paired t-test
hg hg
B) Independent samples t-test
hg hg hg
C) Mann-Whitney U test
hg hg hg
D) One-way ANOVA
hg hg
Answer: B – hg hg
For comparing means of two independent groups with normally distributed data, the indepen
hg hg hg hg hg hg hg hg hg hg hg hg hg
dent samples t-test is appropriate .
hg hg hg hg hg
10. The standard error (SE) differs from the standard deviation (SD) in that:
hg hg hg hg hg hg hg hg hg hg hg hg
A) SE is always larger than SD
hg hg hg hg hg hg
B) SE measures variability of sample means, while SD measures variability of individual observat
hg hg hg hg hg hg hg hg hg hg hg hg hg
ions
C) SE is used for descriptive statistics only
hg hg hg hg hg hg hg
D) SE does not depend on sample size
hg hg hg hg hg hg hg
Answer: B – hg hg
SE is the standard deviation of the sampling distribution of the mean, while SD measures varia
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
bility of individual observations. SE = SD/√n .
hg hg hg hg hg hg hg
Section 3: ANOVA and Regression hg hg hg hg
, 11. In a multiple regression model Y = β₀ + β₁X₁ + β₂X₂ + ε, the coefficient β₁ represents
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
:
A) The change in Y for a 1-unit change in X₁, holding X₂ constant
hg hg hg hg hg hg hg hg hg hg hg hg hg
B) The change in Y for a 1-unit change in X₁, ignoring X₂
hg hg hg hg hg hg hg hg hg hg hg hg
C) The intercept when X₁ = 0
hg hg hg hg hg hg
D) The change in Y for a 1-unit change in X₂
hg hg hg hg hg hg hg hg hg hg
Answer: A – hg hg
In multiple regression, β₁ is the partial regression coefficient representing the change in Y for a
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
1-unit change in X₁ while holding all other variables constant .
hg hg hg hg hg hg hg hg hg hg hg
12. The F-statistic in a one-way ANOVA is calculated as:
hg hg hg hg hg hg hg hg hg
A) MS(between) / MS(within)
hg hg hg
B) MS(within) / MS(between)
hg hg hg
C) SS(between) / SS(within)
hg hg hg
D) SS(total) / SS(between)
hg hg hg
Answer: A – hg hg
F = mean square between groups divided by mean square within (error). A large F suggests gr
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
oup means differ significantly .
hg hg hg hg
13. The degrees of freedom for the chi-
hg hg hg hg hg hg hg
square test of independence in a 3×4 contingency table are:
hg hg hg hg hg hg hg hg hg
A) 12hg
B) 11hg
C) 6 hg
D) 2 hg
Answer: C – df = (r-1)(c-1) = (3-1)(4-1) = 2 × 3 = 6 .
hg hg hg hg hg hg hg hg hg hg hg hg hg hg
14. In a scatterplot, if the points fall exactly on a straight line with a positive slope, the c
hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg hg
orrelation coefficient r equals: hg hg hg
A) 0 hg
B) -1hg
C) +1hg
D) 0.5hg
Answer: C – Perfect positive linear correlation yields r = +1.0 .
hg hg hg hg hg hg hg hg hg hg hg
