DTSA 5002 (Biostatistics II) Statistical Inference Confidence Intervals, and Estimation
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1. What is the purpose of statistical inference? - Correct Answer: To draw
conclusions about a population based on a sample.
2. What is an intrinsic characteristic of statistical inference? - Correct
Answer: It always involves an intrinsic error due to reliance on a sample.
3. What are continuous variables? - Correct Answer: Variables that can
take any value within an interval, such as weight or height.
4. What are discrete variables? - Correct Answer: Variables that take
countable values, such as the number of children.
5. What type of distribution is used for discrete variables? - Correct
Answer: Discrete probability distributions, such as Binomial or Poisson
distributions.
6. What type of distribution is used for continuous variables? - Correct
Answer: Continuous probability distributions, such as Normal or
Exponential distributions.
7. What is a random variable? - Correct Answer: A variable whose values
are determined by the outcomes of a random phenomenon.
,8. What is an estimator? - Correct Answer: A function of the sample used
to approximate a population parameter.
9. What does the sample mean estimate? - Correct Answer: The
population mean (µ).
10.What is the sampling distribution of the sample mean? - Correct
Answer: The distribution formed by the sample means obtained from
repeated sampling.
11.What happens to the variability of the sample mean as the sample size
increases? - Correct Answer: The variability decreases as the sample
size increases.
12.What is the standard error? - Correct Answer: The standard deviation of
the sampling distribution.
13.How is the standard error (SE) calculated? - Correct Answer: SE = σ / √n.
14.What is the relationship between sample size and standard error? -
Correct Answer: Larger sample sizes produce smaller standard errors.
15.What does the sample variance estimate? - Correct Answer: The
population variance (σ²).
16.What is the significance of the sample proportion (p̂ )? - Correct Answer:
It estimates the population proportion (p).
,17.What is the expected value of the sample mean (E[X̄])? - Correct
Answer: E[X̄] = µ.
18.What is the variance of the sample mean (Var[X̄])? - Correct Answer:
Var[X̄] = σ²/n.
19.What is a variable in statistics? - Correct Answer: A characteristic of
interest that can take different values across individuals.
20.Why do we use sampling distributions? - Correct Answer: To
understand the behavior of estimators across different samples.
21.What is the importance of quantifying error in statistical inference? -
Correct Answer: It allows us to control uncertainty and make informed
decisions.
22.What does SE stand for in statistics? - Correct Answer: Standard Error.
23.What is a confidence interval (CI)? - Correct Answer: A range of
plausible values for a population parameter.
24.What is the general structure of a confidence interval? - Correct
Answer: Estimate ± Margin of Error.
25.What formula represents the margin of error in a confidence interval? -
Correct Answer: Critical Value × SE.
26.What does the critical value depend on? - Correct Answer: The
confidence level (or significance level α).
27.If α = 0.05, what is the confidence level? - Correct Answer: 95%.
, 28.What happens to the width of the confidence interval as the confidence
level increases? - Correct Answer: The confidence interval becomes
wider.
29.What does P(L ≤ μ ≤ U) = 1 − α signify? - Correct Answer: The
probability that the confidence interval contains the true population
parameter.
30.What is needed to construct a confidence interval? - Correct Answer:
An estimator, standard error, chosen confidence level, and sampling
distribution.
31.What is the main question when estimating the population mean μ? -
Correct Answer: In what interval is the true population mean likely to lie?
32.What distribution is assumed when constructing a confidence interval for
the mean with known variance? - Correct Answer: Normal distribution.
33.What is the formula for the sample mean? - Correct Answer: X̄ = (ΣXᵢ) /
n.
34.What is a one-sided confidence bound? - Correct Answer: A confidence
bound used when the scientific question is directional.
35.In the example of a physical therapist estimating muscle strength, what was
the sample mean? - Correct Answer: 84.3
What was the confidence level used in the physical therapist's example?
99%
What is the standard deviation (σ) in the physical therapist's example?
12
What is the confidence interval calculated for the physical therapist's example?
(76.30, 92.29)
What was the sample size (n) in the physical therapist's example?
15
Comprehensive Resource To Help You Ace 2026-2027 Exams
Includes Frequently Tested Questions With ELABORATED
100% Correct COMPLETE SOLUTIONS
Guaranteed Pass First Attempt!! Current Update!!
1. What is the purpose of statistical inference? - Correct Answer: To draw
conclusions about a population based on a sample.
2. What is an intrinsic characteristic of statistical inference? - Correct
Answer: It always involves an intrinsic error due to reliance on a sample.
3. What are continuous variables? - Correct Answer: Variables that can
take any value within an interval, such as weight or height.
4. What are discrete variables? - Correct Answer: Variables that take
countable values, such as the number of children.
5. What type of distribution is used for discrete variables? - Correct
Answer: Discrete probability distributions, such as Binomial or Poisson
distributions.
6. What type of distribution is used for continuous variables? - Correct
Answer: Continuous probability distributions, such as Normal or
Exponential distributions.
7. What is a random variable? - Correct Answer: A variable whose values
are determined by the outcomes of a random phenomenon.
,8. What is an estimator? - Correct Answer: A function of the sample used
to approximate a population parameter.
9. What does the sample mean estimate? - Correct Answer: The
population mean (µ).
10.What is the sampling distribution of the sample mean? - Correct
Answer: The distribution formed by the sample means obtained from
repeated sampling.
11.What happens to the variability of the sample mean as the sample size
increases? - Correct Answer: The variability decreases as the sample
size increases.
12.What is the standard error? - Correct Answer: The standard deviation of
the sampling distribution.
13.How is the standard error (SE) calculated? - Correct Answer: SE = σ / √n.
14.What is the relationship between sample size and standard error? -
Correct Answer: Larger sample sizes produce smaller standard errors.
15.What does the sample variance estimate? - Correct Answer: The
population variance (σ²).
16.What is the significance of the sample proportion (p̂ )? - Correct Answer:
It estimates the population proportion (p).
,17.What is the expected value of the sample mean (E[X̄])? - Correct
Answer: E[X̄] = µ.
18.What is the variance of the sample mean (Var[X̄])? - Correct Answer:
Var[X̄] = σ²/n.
19.What is a variable in statistics? - Correct Answer: A characteristic of
interest that can take different values across individuals.
20.Why do we use sampling distributions? - Correct Answer: To
understand the behavior of estimators across different samples.
21.What is the importance of quantifying error in statistical inference? -
Correct Answer: It allows us to control uncertainty and make informed
decisions.
22.What does SE stand for in statistics? - Correct Answer: Standard Error.
23.What is a confidence interval (CI)? - Correct Answer: A range of
plausible values for a population parameter.
24.What is the general structure of a confidence interval? - Correct
Answer: Estimate ± Margin of Error.
25.What formula represents the margin of error in a confidence interval? -
Correct Answer: Critical Value × SE.
26.What does the critical value depend on? - Correct Answer: The
confidence level (or significance level α).
27.If α = 0.05, what is the confidence level? - Correct Answer: 95%.
, 28.What happens to the width of the confidence interval as the confidence
level increases? - Correct Answer: The confidence interval becomes
wider.
29.What does P(L ≤ μ ≤ U) = 1 − α signify? - Correct Answer: The
probability that the confidence interval contains the true population
parameter.
30.What is needed to construct a confidence interval? - Correct Answer:
An estimator, standard error, chosen confidence level, and sampling
distribution.
31.What is the main question when estimating the population mean μ? -
Correct Answer: In what interval is the true population mean likely to lie?
32.What distribution is assumed when constructing a confidence interval for
the mean with known variance? - Correct Answer: Normal distribution.
33.What is the formula for the sample mean? - Correct Answer: X̄ = (ΣXᵢ) /
n.
34.What is a one-sided confidence bound? - Correct Answer: A confidence
bound used when the scientific question is directional.
35.In the example of a physical therapist estimating muscle strength, what was
the sample mean? - Correct Answer: 84.3
What was the confidence level used in the physical therapist's example?
99%
What is the standard deviation (σ) in the physical therapist's example?
12
What is the confidence interval calculated for the physical therapist's example?
(76.30, 92.29)
What was the sample size (n) in the physical therapist's example?
15
