[HBSCOR] HBS CREDENTIAL OF READINESS CORE
Certification Review Guide
Question 1. Which measure of central tendency is most appropriate for a highly skewed
distribution of sales revenue?
A) Mean
B) Median
C) Mode
D) Range
Answer: B
Explanation: The median is resistant to extreme values and therefore better represents the
typical value in a skewed distribution than the mean.
Question 2. In a histogram, what does the height of each bar represent?
A) The total number of observations in the data set
B) The frequency (or count) of observations within a class interval
C) The cumulative frequency up to that interval
D) The mean value of observations in that interval
Answer: B
Explanation: Each bar’s height shows how many data points fall within the corresponding bin.
Question 3. Which of the following variables is nominal?
A) Customer satisfaction rating on a 1‑10 scale
B) Number of units sold per month
C) Type of product (e.g., “tablet”, “laptop”, “smartphone”)
D) Temperature in Celsius
, [HBSCOR] HBS CREDENTIAL OF READINESS CORE
Certification Review Guide
Answer: C
Explanation: Nominal variables categorize observations without any inherent order.
Question 4. A data set has a mean of 50 and a standard deviation of 5. What is the z‑score for a
value of 60?
A) 1.0
B) 1.5
C) 2.0
D) 2.5
Answer: C
Explanation: z = (X‑μ)/σ = (60‑50)/5 = 10/5 = 2.
Question 5. Which percentile corresponds to a z‑score of 0?
A) 25th percentile
B) 50th percentile
C) 75th percentile
D) 100th percentile
Answer: B
Explanation: A z‑score of 0 lies at the mean of the normal distribution, which is the 50th
percentile.
Question 6. The Central Limit Theorem states that the sampling distribution of the sample mean
approaches a normal distribution as the sample size increases, regardless of the shape of the
population distribution. Which condition is essential for the theorem to hold?
A) The population must be normally distributed.
, [HBSCOR] HBS CREDENTIAL OF READINESS CORE
Certification Review Guide
B) The sample size must be at least 30.
C) Observations must be independent.
D) The population variance must be known.
Answer: C
Explanation: Independence of observations is required; the theorem does not require a normal
population or a specific sample size, though n ≥ 30 is a common rule of thumb.
Question 7. A 95 % confidence interval for the population mean is calculated as (22, 28). Which
statement is correct?
A) There is a 95 % probability that the true mean lies between 22 and 28.
B) 95 % of sample means will fall within this interval.
C) If we repeated sampling many times, 95 % of the constructed intervals would contain the
true mean.
D) The interval will shrink if we increase the confidence level.
Answer: C
Explanation: Confidence intervals are about long‑run frequency: 95 % of such intervals will
capture the true parameter.
Question 8. In hypothesis testing, failing to reject the null hypothesis when it is actually false is a
Type II error. Which factor reduces the probability of a Type II error?
A) Increasing the significance level (α)
B) Decreasing the sample size
C) Using a two‑tailed test instead of a one‑tailed test
D) Increasing the effect size
, [HBSCOR] HBS CREDENTIAL OF READINESS CORE
Certification Review Guide
Answer: D
Explanation: Larger true effect sizes make it easier to detect differences, reducing β (the Type II
error probability).
Question 9. An e‑commerce site runs an A/B test where version A converts 4 % of visitors and
version B converts 5 %. The p‑value for the difference is 0.03. At α = 0.05, what is the correct
decision?
A) Fail to reject the null hypothesis; no difference.
B) Reject the null hypothesis; version B performs better.
C) Accept the alternative hypothesis without further testing.
D) Increase the sample size before making any decision.
Answer: B
Explanation: Since p = 0.03 < 0.05, we reject the null hypothesis and conclude a statistically
significant difference.
Question 10. In simple linear regression, the coefficient of determination (R²) of 0.64 indicates
that:
A) 64 % of the variation in the dependent variable is explained by the independent variable.
B) The regression line predicts the dependent variable with 64 % accuracy.
C) 36 % of the data points lie exactly on the regression line.
D) The slope of the regression line is 0.64.
Answer: A
Explanation: R² measures the proportion of variance in Y accounted for by X.
Certification Review Guide
Question 1. Which measure of central tendency is most appropriate for a highly skewed
distribution of sales revenue?
A) Mean
B) Median
C) Mode
D) Range
Answer: B
Explanation: The median is resistant to extreme values and therefore better represents the
typical value in a skewed distribution than the mean.
Question 2. In a histogram, what does the height of each bar represent?
A) The total number of observations in the data set
B) The frequency (or count) of observations within a class interval
C) The cumulative frequency up to that interval
D) The mean value of observations in that interval
Answer: B
Explanation: Each bar’s height shows how many data points fall within the corresponding bin.
Question 3. Which of the following variables is nominal?
A) Customer satisfaction rating on a 1‑10 scale
B) Number of units sold per month
C) Type of product (e.g., “tablet”, “laptop”, “smartphone”)
D) Temperature in Celsius
, [HBSCOR] HBS CREDENTIAL OF READINESS CORE
Certification Review Guide
Answer: C
Explanation: Nominal variables categorize observations without any inherent order.
Question 4. A data set has a mean of 50 and a standard deviation of 5. What is the z‑score for a
value of 60?
A) 1.0
B) 1.5
C) 2.0
D) 2.5
Answer: C
Explanation: z = (X‑μ)/σ = (60‑50)/5 = 10/5 = 2.
Question 5. Which percentile corresponds to a z‑score of 0?
A) 25th percentile
B) 50th percentile
C) 75th percentile
D) 100th percentile
Answer: B
Explanation: A z‑score of 0 lies at the mean of the normal distribution, which is the 50th
percentile.
Question 6. The Central Limit Theorem states that the sampling distribution of the sample mean
approaches a normal distribution as the sample size increases, regardless of the shape of the
population distribution. Which condition is essential for the theorem to hold?
A) The population must be normally distributed.
, [HBSCOR] HBS CREDENTIAL OF READINESS CORE
Certification Review Guide
B) The sample size must be at least 30.
C) Observations must be independent.
D) The population variance must be known.
Answer: C
Explanation: Independence of observations is required; the theorem does not require a normal
population or a specific sample size, though n ≥ 30 is a common rule of thumb.
Question 7. A 95 % confidence interval for the population mean is calculated as (22, 28). Which
statement is correct?
A) There is a 95 % probability that the true mean lies between 22 and 28.
B) 95 % of sample means will fall within this interval.
C) If we repeated sampling many times, 95 % of the constructed intervals would contain the
true mean.
D) The interval will shrink if we increase the confidence level.
Answer: C
Explanation: Confidence intervals are about long‑run frequency: 95 % of such intervals will
capture the true parameter.
Question 8. In hypothesis testing, failing to reject the null hypothesis when it is actually false is a
Type II error. Which factor reduces the probability of a Type II error?
A) Increasing the significance level (α)
B) Decreasing the sample size
C) Using a two‑tailed test instead of a one‑tailed test
D) Increasing the effect size
, [HBSCOR] HBS CREDENTIAL OF READINESS CORE
Certification Review Guide
Answer: D
Explanation: Larger true effect sizes make it easier to detect differences, reducing β (the Type II
error probability).
Question 9. An e‑commerce site runs an A/B test where version A converts 4 % of visitors and
version B converts 5 %. The p‑value for the difference is 0.03. At α = 0.05, what is the correct
decision?
A) Fail to reject the null hypothesis; no difference.
B) Reject the null hypothesis; version B performs better.
C) Accept the alternative hypothesis without further testing.
D) Increase the sample size before making any decision.
Answer: B
Explanation: Since p = 0.03 < 0.05, we reject the null hypothesis and conclude a statistically
significant difference.
Question 10. In simple linear regression, the coefficient of determination (R²) of 0.64 indicates
that:
A) 64 % of the variation in the dependent variable is explained by the independent variable.
B) The regression line predicts the dependent variable with 64 % accuracy.
C) 36 % of the data points lie exactly on the regression line.
D) The slope of the regression line is 0.64.
Answer: A
Explanation: R² measures the proportion of variance in Y accounted for by X.
