QMB 3200 Final Exam UCF Practice
QUESTIONS AND CORRECT ANSWERS
(VERIFIED ANSWERS) PLUS RATIONALES
2025
1. The mean of a sample of 25 observations is 50, and the standard
deviation is 5. What is the standard error of the mean?
A) 1.00
B) 0.20
C) 1.00
D) 2.00
The standard error is calculated as σ/√n = 5/√25 = 5/5 = 1.00.
2. If the level of significance is 0.05, what is the probability of making a
Type I error?
A) 0.10
B) 0.05
, C) 0.95
D) 0.50
By definition, the level of significance (α) is the probability of
rejecting a true null hypothesis, which is a Type I error.
3. In hypothesis testing, which of the following is true if the p-value is
less than α?
A) Do not reject the null hypothesis
B) Accept the null hypothesis
C) Reject the null hypothesis
D) None of the above
If p-value < α, there is enough evidence to reject H0 in favor of Ha.
4. Which of these is a point estimator for the population mean?
A) Population mean
B) Sample mean
C) Standard deviation
D) Population proportion
A point estimator uses sample data to estimate a population
parameter; the sample mean estimates the population mean.
,5. If the correlation coefficient is -0.85, what does this imply?
A) A weak negative relationship
B) A weak positive relationship
C) A strong positive relationship
D) A strong negative relationship
Correlation coefficients close to -1 indicate a strong negative linear
relationship.
6. What is the purpose of using the t-distribution instead of the normal z-
distribution?
A) When the population standard deviation is known
B) When the population mean is unknown
C) When the population standard deviation is unknown and sample
size is small
D) For all large samples
The t-distribution is used when σ is unknown and n is small (typically
n < 30).
7. A confidence interval for a mean is 45 to 55. What is the point
estimate?
A) 45
B) 55
C) 50
, D) 10
The point estimate is the midpoint: (45 + 55)/2 = 50.
8. A manager wants to know if a new process reduces defects. Which is
the correct alternative hypothesis?
A) μ ≥ μ₀
B) μ = μ₀
C) μ ≤ μ₀
D) μ < μ₀
To test if the mean is less than the current mean, the alternative
must be μ < μ₀.
9. In regression analysis, what does the coefficient of determination (R²)
represent?
A) The slope
B) The intercept
C) The proportion of variability explained by the model
D) The residual
R² measures how well the regression line fits the data by explaining
the variance.
QUESTIONS AND CORRECT ANSWERS
(VERIFIED ANSWERS) PLUS RATIONALES
2025
1. The mean of a sample of 25 observations is 50, and the standard
deviation is 5. What is the standard error of the mean?
A) 1.00
B) 0.20
C) 1.00
D) 2.00
The standard error is calculated as σ/√n = 5/√25 = 5/5 = 1.00.
2. If the level of significance is 0.05, what is the probability of making a
Type I error?
A) 0.10
B) 0.05
, C) 0.95
D) 0.50
By definition, the level of significance (α) is the probability of
rejecting a true null hypothesis, which is a Type I error.
3. In hypothesis testing, which of the following is true if the p-value is
less than α?
A) Do not reject the null hypothesis
B) Accept the null hypothesis
C) Reject the null hypothesis
D) None of the above
If p-value < α, there is enough evidence to reject H0 in favor of Ha.
4. Which of these is a point estimator for the population mean?
A) Population mean
B) Sample mean
C) Standard deviation
D) Population proportion
A point estimator uses sample data to estimate a population
parameter; the sample mean estimates the population mean.
,5. If the correlation coefficient is -0.85, what does this imply?
A) A weak negative relationship
B) A weak positive relationship
C) A strong positive relationship
D) A strong negative relationship
Correlation coefficients close to -1 indicate a strong negative linear
relationship.
6. What is the purpose of using the t-distribution instead of the normal z-
distribution?
A) When the population standard deviation is known
B) When the population mean is unknown
C) When the population standard deviation is unknown and sample
size is small
D) For all large samples
The t-distribution is used when σ is unknown and n is small (typically
n < 30).
7. A confidence interval for a mean is 45 to 55. What is the point
estimate?
A) 45
B) 55
C) 50
, D) 10
The point estimate is the midpoint: (45 + 55)/2 = 50.
8. A manager wants to know if a new process reduces defects. Which is
the correct alternative hypothesis?
A) μ ≥ μ₀
B) μ = μ₀
C) μ ≤ μ₀
D) μ < μ₀
To test if the mean is less than the current mean, the alternative
must be μ < μ₀.
9. In regression analysis, what does the coefficient of determination (R²)
represent?
A) The slope
B) The intercept
C) The proportion of variability explained by the model
D) The residual
R² measures how well the regression line fits the data by explaining
the variance.
