COMM 214 FINAL EXAM PREP QUESTIONS COMPLETE
WITH 100% VERIFIED ANSWERS
1. In hypothesis testing, what does a small p-value indicate?
a) The test statistic is not extreme
b) High variability in the data
c) The test was conducted incorrectly
d) The null hypothesis is true
e) Strong evidence against the null hypothesis
Rationale: A small p-value (typically ≤ 0.05) suggests that the observed
data are unlikely under the null hypothesis, providing strong evidence
to reject H₀.
2. Which of the following describes a 95% confidence interval?
a) There is a 95% chance that the sample mean is correct
b) The interval includes the sample mean
c) 95% of the sample data lies within the interval
d) 95% of values will always lie within this interval
e) We are 95% confident that the population parameter lies within the
interval
Rationale: A 95% confidence interval means that if we took many
samples, 95% of the intervals constructed would contain the true
population parameter.
,3. You draw two cards from a standard deck without replacement.
What is the probability both are aces?
a) 1/169
b) 1/26
c) 1/13
d) 1/221
e) 1/52
Rationale: P(1st Ace) = 4/52; P(2nd Ace | 1st Ace) = 3/51; product =
(4/52)*(3/51) = 12/2652 = 1/221.
4. The Central Limit Theorem tells us:
a) The population distribution must be normal
b) Sample distributions become skewed with large n
c) The mean of a population equals the median
d) Variance of the population must be zero
e) The sampling distribution of the mean becomes normal as n
increases
Rationale: The CLT states that for sufficiently large sample sizes, the
sampling distribution of the sample mean approaches a normal
distribution regardless of the population’s distribution.
5. What is the standard deviation of the dataset: 4, 6, 8, 10, 12?
a) 2.5
b) 2.82
c) 3.16
d) 4.00
e) 5.00
,Rationale: Mean = 8. Deviations squared: (16+4+0+4+16)=40.
Population variance = 40/5=8, SD = √8 ≈ 2.828.
6. What does an R² of 0.85 mean in regression?
a) 85% of the residuals are significant
b) The model predicts 85% of the values accurately
c) There’s an 85% chance the model is correct
d) 85% of the data lies on the regression line
e) 85% of the variation in Y is explained by the model
Rationale: R² represents the proportion of variance in the dependent
variable that is predictable from the independent variable(s).
7. In a one-sample z-test, which of the following affects the standard
error?
a) Sample mean
b) Population mean
c) Sample size
d) t-distribution
e) Confidence level
Rationale: Standard error = σ/√n; thus sample size (n) directly affects it.
Larger n reduces standard error.
8. Type I error is:
a) Accepting Ho when it is false
b) Rejecting Ho when it is true
c) Accepting IL when it is false
, d) Rejecting HL when it is true
e) Failing to reject Ho when it is false
Rationale: Type I error (α) occurs when we reject a true null hypothesis.
9. If the probability of rain on a given day is 0.4, what is the
probability it does not rain for three consecutive days (assuming
independence)?
a) 0.064
b) 0.216
c) 0.2744
d) 0.512
e) 0.6
Rationale: P(no rain) = 0.6. For 3 days: 0.6³ = 0.216.
10. What increases the power of a hypothesis test?
a) Decreasing sample size
b) Increasing significance level
c) Increasing standard error
d) Decreasing population mean
e) Using a smaller p-value threshold
Rationale: Increasing α (significance level) increases the rejection
region, thus increasing power (1-β). Larger sample size also increases
power, but that option isn’t listed.
11. A 90% confidence interval for a population mean is (15, 25). What
is the margin of error?
WITH 100% VERIFIED ANSWERS
1. In hypothesis testing, what does a small p-value indicate?
a) The test statistic is not extreme
b) High variability in the data
c) The test was conducted incorrectly
d) The null hypothesis is true
e) Strong evidence against the null hypothesis
Rationale: A small p-value (typically ≤ 0.05) suggests that the observed
data are unlikely under the null hypothesis, providing strong evidence
to reject H₀.
2. Which of the following describes a 95% confidence interval?
a) There is a 95% chance that the sample mean is correct
b) The interval includes the sample mean
c) 95% of the sample data lies within the interval
d) 95% of values will always lie within this interval
e) We are 95% confident that the population parameter lies within the
interval
Rationale: A 95% confidence interval means that if we took many
samples, 95% of the intervals constructed would contain the true
population parameter.
,3. You draw two cards from a standard deck without replacement.
What is the probability both are aces?
a) 1/169
b) 1/26
c) 1/13
d) 1/221
e) 1/52
Rationale: P(1st Ace) = 4/52; P(2nd Ace | 1st Ace) = 3/51; product =
(4/52)*(3/51) = 12/2652 = 1/221.
4. The Central Limit Theorem tells us:
a) The population distribution must be normal
b) Sample distributions become skewed with large n
c) The mean of a population equals the median
d) Variance of the population must be zero
e) The sampling distribution of the mean becomes normal as n
increases
Rationale: The CLT states that for sufficiently large sample sizes, the
sampling distribution of the sample mean approaches a normal
distribution regardless of the population’s distribution.
5. What is the standard deviation of the dataset: 4, 6, 8, 10, 12?
a) 2.5
b) 2.82
c) 3.16
d) 4.00
e) 5.00
,Rationale: Mean = 8. Deviations squared: (16+4+0+4+16)=40.
Population variance = 40/5=8, SD = √8 ≈ 2.828.
6. What does an R² of 0.85 mean in regression?
a) 85% of the residuals are significant
b) The model predicts 85% of the values accurately
c) There’s an 85% chance the model is correct
d) 85% of the data lies on the regression line
e) 85% of the variation in Y is explained by the model
Rationale: R² represents the proportion of variance in the dependent
variable that is predictable from the independent variable(s).
7. In a one-sample z-test, which of the following affects the standard
error?
a) Sample mean
b) Population mean
c) Sample size
d) t-distribution
e) Confidence level
Rationale: Standard error = σ/√n; thus sample size (n) directly affects it.
Larger n reduces standard error.
8. Type I error is:
a) Accepting Ho when it is false
b) Rejecting Ho when it is true
c) Accepting IL when it is false
, d) Rejecting HL when it is true
e) Failing to reject Ho when it is false
Rationale: Type I error (α) occurs when we reject a true null hypothesis.
9. If the probability of rain on a given day is 0.4, what is the
probability it does not rain for three consecutive days (assuming
independence)?
a) 0.064
b) 0.216
c) 0.2744
d) 0.512
e) 0.6
Rationale: P(no rain) = 0.6. For 3 days: 0.6³ = 0.216.
10. What increases the power of a hypothesis test?
a) Decreasing sample size
b) Increasing significance level
c) Increasing standard error
d) Decreasing population mean
e) Using a smaller p-value threshold
Rationale: Increasing α (significance level) increases the rejection
region, thus increasing power (1-β). Larger sample size also increases
power, but that option isn’t listed.
11. A 90% confidence interval for a population mean is (15, 25). What
is the margin of error?
