Academic Year 2026–2027 UNISA Assignment: QMI5100 Quantitative
Support 5 Fully Solved Assignment with Verified Answers | Advanced
Quantitative Analysis, Statistical Methods, Data Interpretation, Decision-
Making Models, Business Analytics and Quantitative Problem Solving
,Question 1: In the context of quantitative support, which of the following best describes
the primary distinction between a parameter and a statistic?
A. A parameter describes a sample, while a statistic describes a population.
B. A parameter is a random variable, while a statistic is a fixed constant.
C. A parameter describes a population, while a statistic describes a sample.
D. A parameter is always known, while a statistic must be estimated.
CORRECT ANSWER: C. A parameter describes a population, while a statistic describes a
sample.
Rationale: In statistics, a parameter is a numerical characteristic of a population (e.g.,
population mean μ), while a statistic is a numerical characteristic of a sample (e.g., sample
mean ̄ x). This distinction is fundamental to inferential statistics, where we use sample statistics
to estimate population parameters.
Question 2: A researcher is analyzing the relationship between two continuous variables
and wants to measure both the strength and direction of their linear association. Which
statistical measure is most appropriate?
A. Chi-square test statistic
B. Spearman's rank correlation coefficient
C. Pearson's correlation coefficient
D. Coefficient of determination
CORRECT ANSWER: C. Pearson's correlation coefficient
Rationale: Pearson's correlation coefficient (r) quantifies both the strength and direction of a
linear relationship between two continuous variables. It ranges from -1 to +1, with the sign
indicating direction and the absolute value indicating strength. Spearman's is for ordinal or non-
linear relationships; chi-square tests association between categorical variables.
Question 3: A dataset contains outliers that are heavily influencing the mean. Which
measure of central tendency would be most robust and appropriate for summarizing the
typical value of this dataset?
A. Mean
B. Median
C. Mode
D. Geometric mean
CORRECT ANSWER: B. Median
Rationale: The median is the middle value when data are ordered and is resistant to outliers
because it depends only on the position of values, not their magnitude. The mean is sensitive to
extreme values, and the mode may not represent the center. The geometric mean is sensitive to
zero and negative values.
Question 4: Which of the following probability distributions is most appropriate for
modeling the number of defects in a fixed-length roll of wire, where defects occur
independently and at a constant average rate?
A. Binomial distribution
B. Poisson distribution
,C. Normal distribution
D. Exponential distribution
CORRECT ANSWER: B. Poisson distribution
Rationale: The Poisson distribution models the count of independent events occurring in a fixed
interval of time or space when events occur at a constant average rate. The binomial models
counts in a fixed number of trials, the normal is for continuous data, and the exponential
models waiting times between events.
Question 5: In hypothesis testing, a p-value of 0.03 is obtained. Assuming a significance
level (α) of 0.05, what is the correct decision and interpretation?
A. Fail to reject the null hypothesis; there is insufficient evidence against it.
B. Reject the null hypothesis; the result is statistically significant.
C. Reject the alternative hypothesis; the result is not significant.
D. Fail to reject the null hypothesis; the result is statistically significant.
CORRECT ANSWER: B. Reject the null hypothesis; the result is statistically significant.
Rationale: Since the p-value (0.03) is less than the significance level (0.05), we reject the null
hypothesis. This indicates that the observed data are unlikely under the null hypothesis,
providing sufficient statistical evidence to support the alternative hypothesis.
Question 6: A 95% confidence interval for a population mean is calculated as (45.2, 58.6).
Which of the following interpretations is correct?
A. There is a 95% probability that the true population mean lies between 45.2 and 58.6.
B. 95% of the sample data falls between 45.2 and 58.6.
C. We are 95% confident that the interval (45.2, 58.6) contains the true population mean.
D. The sample mean has a 95% chance of falling between 45.2 and 58.6.
CORRECT ANSWER: C. We are 95% confident that the interval (45.2, 58.6) contains the true
population mean.
Rationale: The correct interpretation of a confidence interval is in terms of confidence in the
procedure: if we repeated the sampling many times, approximately 95% of such intervals would
contain the true population mean. The interval itself either contains the mean or not; probability
is not assigned to the fixed interval.
Question 7: Which type of sampling method involves dividing the population into
subgroups (strata) and then randomly selecting samples from each subgroup in proportion
to their size?
A. Simple random sampling
B. Systematic sampling
C. Stratified random sampling
D. Cluster sampling
CORRECT ANSWER: C. Stratified random sampling
Rationale: Stratified random sampling divides the population into homogeneous subgroups
(strata) based on a characteristic (e.g., age, income) and then draws a random sample from
, each stratum, often proportionally. This ensures representation of all subgroups. Cluster
sampling divides into heterogeneous groups and samples entire clusters.
Question 8: A data analyst notices that the variance of a dataset is 144. What is the
standard deviation of this dataset?
A. 12
B. 14.4
C. 144
D. 20,736
CORRECT ANSWER: A. 12
Rationale: The standard deviation is the positive square root of the variance. Therefore, the
standard deviation = √144 = 12. Standard deviation is in the same units as the original data,
making it more interpretable than variance.
Question 9: In a regression analysis, the coefficient of determination (R²) is 0.81. What
does this value indicate about the model's fit?
A. The model explains 81% of the variation in the dependent variable.
B. The correlation coefficient is 0.81.
C. The model explains 19% of the variation in the dependent variable.
D. The model has a strong positive slope.
CORRECT ANSWER: A. The model explains 81% of the variation in the dependent variable.
Rationale: R² represents the proportion of variance in the dependent variable that is predictable
from the independent variable(s). An R² of 0.81 means 81% of the total variation in the response
variable is explained by the model. The correlation coefficient would be r = ±√0.81 = ±0.90.
Question 10: Which of the following is an assumption of a simple linear regression model
regarding the errors (residuals)?
A. Errors are normally distributed with a mean of 1.
B. Errors are independent and identically distributed with a mean of 0 and constant variance.
C. Errors are correlated with the independent variable.
D. Errors have a non-constant variance that increases with the fitted values.
CORRECT ANSWER: B. Errors are independent and identically distributed with a mean of 0
and constant variance.
Rationale: The key assumptions for linear regression errors (residuals) are: 1) mean of zero, 2)
constant variance (homoscedasticity), 3) independence, and 4) normality (for inference). The
errors should not be correlated with predictors; non-constant variance violates
homoscedasticity.
Question 11: A pharmaceutical company tests a new drug and obtains a 99% confidence
interval for the mean reduction in blood pressure as (8.5, 12.3) mmHg. Which of the
following statements is true?
A. The probability is 0.99 that the mean reduction in blood pressure is between 8.5 and 12.3
mmHg.
B. The margin of error for this interval is 1.9 mmHg.
Support 5 Fully Solved Assignment with Verified Answers | Advanced
Quantitative Analysis, Statistical Methods, Data Interpretation, Decision-
Making Models, Business Analytics and Quantitative Problem Solving
,Question 1: In the context of quantitative support, which of the following best describes
the primary distinction between a parameter and a statistic?
A. A parameter describes a sample, while a statistic describes a population.
B. A parameter is a random variable, while a statistic is a fixed constant.
C. A parameter describes a population, while a statistic describes a sample.
D. A parameter is always known, while a statistic must be estimated.
CORRECT ANSWER: C. A parameter describes a population, while a statistic describes a
sample.
Rationale: In statistics, a parameter is a numerical characteristic of a population (e.g.,
population mean μ), while a statistic is a numerical characteristic of a sample (e.g., sample
mean ̄ x). This distinction is fundamental to inferential statistics, where we use sample statistics
to estimate population parameters.
Question 2: A researcher is analyzing the relationship between two continuous variables
and wants to measure both the strength and direction of their linear association. Which
statistical measure is most appropriate?
A. Chi-square test statistic
B. Spearman's rank correlation coefficient
C. Pearson's correlation coefficient
D. Coefficient of determination
CORRECT ANSWER: C. Pearson's correlation coefficient
Rationale: Pearson's correlation coefficient (r) quantifies both the strength and direction of a
linear relationship between two continuous variables. It ranges from -1 to +1, with the sign
indicating direction and the absolute value indicating strength. Spearman's is for ordinal or non-
linear relationships; chi-square tests association between categorical variables.
Question 3: A dataset contains outliers that are heavily influencing the mean. Which
measure of central tendency would be most robust and appropriate for summarizing the
typical value of this dataset?
A. Mean
B. Median
C. Mode
D. Geometric mean
CORRECT ANSWER: B. Median
Rationale: The median is the middle value when data are ordered and is resistant to outliers
because it depends only on the position of values, not their magnitude. The mean is sensitive to
extreme values, and the mode may not represent the center. The geometric mean is sensitive to
zero and negative values.
Question 4: Which of the following probability distributions is most appropriate for
modeling the number of defects in a fixed-length roll of wire, where defects occur
independently and at a constant average rate?
A. Binomial distribution
B. Poisson distribution
,C. Normal distribution
D. Exponential distribution
CORRECT ANSWER: B. Poisson distribution
Rationale: The Poisson distribution models the count of independent events occurring in a fixed
interval of time or space when events occur at a constant average rate. The binomial models
counts in a fixed number of trials, the normal is for continuous data, and the exponential
models waiting times between events.
Question 5: In hypothesis testing, a p-value of 0.03 is obtained. Assuming a significance
level (α) of 0.05, what is the correct decision and interpretation?
A. Fail to reject the null hypothesis; there is insufficient evidence against it.
B. Reject the null hypothesis; the result is statistically significant.
C. Reject the alternative hypothesis; the result is not significant.
D. Fail to reject the null hypothesis; the result is statistically significant.
CORRECT ANSWER: B. Reject the null hypothesis; the result is statistically significant.
Rationale: Since the p-value (0.03) is less than the significance level (0.05), we reject the null
hypothesis. This indicates that the observed data are unlikely under the null hypothesis,
providing sufficient statistical evidence to support the alternative hypothesis.
Question 6: A 95% confidence interval for a population mean is calculated as (45.2, 58.6).
Which of the following interpretations is correct?
A. There is a 95% probability that the true population mean lies between 45.2 and 58.6.
B. 95% of the sample data falls between 45.2 and 58.6.
C. We are 95% confident that the interval (45.2, 58.6) contains the true population mean.
D. The sample mean has a 95% chance of falling between 45.2 and 58.6.
CORRECT ANSWER: C. We are 95% confident that the interval (45.2, 58.6) contains the true
population mean.
Rationale: The correct interpretation of a confidence interval is in terms of confidence in the
procedure: if we repeated the sampling many times, approximately 95% of such intervals would
contain the true population mean. The interval itself either contains the mean or not; probability
is not assigned to the fixed interval.
Question 7: Which type of sampling method involves dividing the population into
subgroups (strata) and then randomly selecting samples from each subgroup in proportion
to their size?
A. Simple random sampling
B. Systematic sampling
C. Stratified random sampling
D. Cluster sampling
CORRECT ANSWER: C. Stratified random sampling
Rationale: Stratified random sampling divides the population into homogeneous subgroups
(strata) based on a characteristic (e.g., age, income) and then draws a random sample from
, each stratum, often proportionally. This ensures representation of all subgroups. Cluster
sampling divides into heterogeneous groups and samples entire clusters.
Question 8: A data analyst notices that the variance of a dataset is 144. What is the
standard deviation of this dataset?
A. 12
B. 14.4
C. 144
D. 20,736
CORRECT ANSWER: A. 12
Rationale: The standard deviation is the positive square root of the variance. Therefore, the
standard deviation = √144 = 12. Standard deviation is in the same units as the original data,
making it more interpretable than variance.
Question 9: In a regression analysis, the coefficient of determination (R²) is 0.81. What
does this value indicate about the model's fit?
A. The model explains 81% of the variation in the dependent variable.
B. The correlation coefficient is 0.81.
C. The model explains 19% of the variation in the dependent variable.
D. The model has a strong positive slope.
CORRECT ANSWER: A. The model explains 81% of the variation in the dependent variable.
Rationale: R² represents the proportion of variance in the dependent variable that is predictable
from the independent variable(s). An R² of 0.81 means 81% of the total variation in the response
variable is explained by the model. The correlation coefficient would be r = ±√0.81 = ±0.90.
Question 10: Which of the following is an assumption of a simple linear regression model
regarding the errors (residuals)?
A. Errors are normally distributed with a mean of 1.
B. Errors are independent and identically distributed with a mean of 0 and constant variance.
C. Errors are correlated with the independent variable.
D. Errors have a non-constant variance that increases with the fitted values.
CORRECT ANSWER: B. Errors are independent and identically distributed with a mean of 0
and constant variance.
Rationale: The key assumptions for linear regression errors (residuals) are: 1) mean of zero, 2)
constant variance (homoscedasticity), 3) independence, and 4) normality (for inference). The
errors should not be correlated with predictors; non-constant variance violates
homoscedasticity.
Question 11: A pharmaceutical company tests a new drug and obtains a 99% confidence
interval for the mean reduction in blood pressure as (8.5, 12.3) mmHg. Which of the
following statements is true?
A. The probability is 0.99 that the mean reduction in blood pressure is between 8.5 and 12.3
mmHg.
B. The margin of error for this interval is 1.9 mmHg.
