Question 1

Which of the following best describes the primary purpose of using sampling in business statistics?

Accepted Answer

To estimate population parameters efficiently when it is impractical to survey the entire population.

Question 2

A company wants to compare the average sales of two different regions. Which statistical method should they use to determine if the difference in means is significant?

Accepted Answer

Hypothesis test for means

Question 3

Which formula is used to calculate the sample mean $$\bar{x}$$ from a set of $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 4

A survey is conducted to estimate the proportion of customers satisfied with a new product. Which type of variable is being measured?

Accepted Answer

Categorical (qualitative)

Question 5

Which of the following is NOT a valid reason for using random sampling in business statistics?

Accepted Answer

To guarantee that every possible sample will yield the same result

Question 6

A business analyst uses the following formula to calculate the sample variance $$s^2$$:

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

What does the denominator $$n-1$$ represent?

Accepted Answer

The degrees of freedom in the sample

Question 7

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize data; inferential statistics draw conclusions about populations based on samples.

Question 8

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

Accepted Answer

Regression analysis

Question 9

If the probability of a customer making a purchase is $$0.3$$, what is the probability that out of 5 customers, exactly 2 will make a purchase? (Assume independence)

Accepted Answer

$$P = \binom{5}{2} (0.3)^2$ (0.7)^3$ = 0.3087$$

Question 10

Which formula is used to calculate a 95% confidence interval for the population mean $$\mu$$ when the sample mean is $$\bar{x}$$, the sample standard deviation is $$s$$, and the sample size is $$n$$?

Accepted Answer

$$\bar{x} \pm z_{0.025} \frac{s}{\sqrt{n}}$$

Question 11

A business wants to test if a new training program increases employee productivity. Which is the correct null hypothesis $$H_0$$ for this scenario?

Accepted Answer

$$H_0$$: \mu_{new} = \mu_{old}$$

Question 12

Which of the following is an example of a discrete random variable in a business context?

Accepted Answer

The number of defective products in a batch

Question 13

A correlation coefficient $$r$$ between advertising spend and sales is found to be $$0.85. $$What does this indicate?

Accepted Answer

There is a strong positive linear relationship between advertising spend and sales.

Question 14

Which formula is used to calculate the expected value $$E(X) of a $$discrete random variable $$X$$ with possible values $$x_i$$ and probabilities $$p_i$$?

Accepted Answer

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

Question 15

A business manager wants to know if customer satisfaction scores differ between two stores. Which statistical test should be used?

Accepted Answer

Two-sample t-test

Question 16

Which of the following statements about the Central Limit Theorem is correct?

Accepted Answer

The sampling distribution of the sample mean approaches normality as sample size increases, regardless of the population's distribution.

Question 17

A company collects data on the number of products sold each day. Which chapter from the course outline would most likely cover methods for summarizing and describing this quantitative data?

Accepted Answer

Chapter 4: Exploring and Describing Quantitative Data

Question 18

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 19

A business analyst wants to estimate the proportion of customers who prefer a new product. Which formula should be used to calculate the standard error of the sample proportion $$\hat{p}$$?

Accepted Answer

$$SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

EC285C: Introductory Statistics – Syllabus and Study Guide

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