Q: Which formula would you use to calculate the probability of event $$A$$ and event $$B$$ both occurring, assuming they are independent?

$$P(A \cap B) = P(A) \times P(B)$$

Question 1

Which of the following best describes the primary goal of statistics in business decision-making?

Accepted Answer

To extract insights and make meaningful inferences and predictions from data.

Question 2

A manager wants to determine if a new marketing strategy has increased sales. Which statistical method should they use to compare sales before and after the strategy implementation?

Accepted Answer

Hypothesis testing

Question 3

Which formula would you use to calculate the sample mean $$\bar{x} of a $$dataset with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 4

A company wants to predict future sales based on advertising spend. Which statistical technique is most appropriate?

Accepted Answer

Simple linear regression

Question 5

Which of the following is the correct formula for the standard deviation $$s of a $$sample?

Accepted Answer

$$s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2$}{n-1}}$$

Question 6

In the context of business analytics, what is the main purpose of using data visualization tools like Tableau?

Accepted Answer

To help communicate complex data insights in a clear and accessible way.

Question 7

A pharmaceutical company tests a new drug and wants to know if the observed effect is due to the drug or just random chance. Which statistical concept is most relevant?

Accepted Answer

Statistical significance

Question 8

Which formula represents the confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

$$\bar{x} \pm t^* \frac{s}{\sqrt{n}}$$

Question 9

A quality control manager uses a random sample of products to estimate the defect rate in a factory. Which statistical concept is being applied?

Accepted Answer

Sampling distribution

Question 10

Which of the following best describes the purpose of hypothesis testing in business analytics?

Accepted Answer

To make decisions about a population based on sample data.

Question 11

A retail chain wants to understand the relationship between store size and annual revenue. Which statistical method should they use?

Accepted Answer

Simple linear regression

Question 12

Which formula would you use to calculate the probability of event $$A$$ and event $$B$$ both occurring, assuming they are independent?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Question 13

A hospital administrator wants to forecast the number of patients for the next month based on historical data. Which statistical technique is most appropriate?

Accepted Answer

Forecasting

Question 14

Which formula is used to calculate the correlation coefficient $$r$$ between two variables $$x$$ and $$y$$?

Accepted Answer

$$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2$ \sum (y_i - \bar{y})^2$}}$$

Question 15

A business analyst uses Excel’s Data Analysis ToolPak to perform a regression analysis. What is the main advantage of using such software?

Accepted Answer

It automates calculations and allows for more complex analyses.

Question 16

Which formula would you use to calculate the expected value $$E(X) of a $$discrete random variable $$X$$ with possible values $$x_1$$, $$x_2$$, ..., x_n$$ and probabilities p_1$, p_2$, ..., p_n$$?

Accepted Answer

$$E(X) = \sum_{i=1}^{n} x_i p_i$$

Question 17

A company wants to determine if the average time to assemble a product has decreased after a new training program. Which statistical test should they use?

Accepted Answer

A paired t-test

Question 18

Which formula represents the equation of a simple linear regression line?

Accepted Answer

$$\hat{y} = b_0$ + b_1$ x$$

Question 19

A data scientist is building a model to predict whether a customer will buy a product (yes/no). Which statistical method is most appropriate?

Accepted Answer

Logistic regression

Question 20

Which formula would you use to calculate the margin of error for a 95% confidence interval for a population mean, given sample standard deviation $$s$$ and sample size $$n$$?

Accepted Answer

$$t^* \frac{s}{\sqrt{n}}$$

Data Analytics for Business: Syllabus and Course Overview (BA 6474 705, Fall 2026)

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