Question 1

Which of the following best describes the primary objective of business statistics as outlined in the course materials?

Accepted Answer

To build analytic skills through the analysis of data, enabling data-driven decisions for organizations.

Question 2

A company wants to summarize its monthly sales data using a graph. Which type of graph would be most appropriate for displaying the frequency of sales in different ranges?

Accepted Answer

Histogram

Question 3

Which formula correctly calculates the sample mean $$\bar{x}$$ for 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 business analyst is interested in the variability of customer wait times. Which measure should they use to quantify this variability?

Accepted Answer

Standard deviation

Question 5

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 and use the binomial formula)

Accepted Answer

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

Question 6

Which of the following is NOT a requirement for using the normal approximation to the binomial distribution?

Accepted Answer

The probability $$p$$ must be close to 0 or 1.

Question 7

A manager wants to estimate the average time employees spend on a task. Which hypothesis test should they use?

Accepted Answer

Hypothesis test for means

Question 8

Which formula represents the sample variance $$s^2$$ for a dataset with $$n$$ observations?

Accepted Answer

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

Question 9

A business wants to test if the proportion of customers satisfied with their service is greater than 80%. Which is the correct null hypothesis $$H_0$$?

Accepted Answer

$$H_0$$: p = 0.8$$

Question 10

Which of the following best describes a Type II error in hypothesis testing?

Accepted Answer

Failing to reject a false null hypothesis

Question 11

A company collects data on advertising spend and sales revenue. Which statistical technique should they use to analyze the relationship between these two variables?

Accepted Answer

Simple linear regression

Question 12

Which formula is used to calculate the $$z-$$score for a value $$x in a $$dataset with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 13

A business analyst wants to display the relationship between two quantitative variables. Which type of graph should they use?

Accepted Answer

Scatter plot

Question 14

If a sample of 100 customers has a mean satisfaction score of 4.2 and a standard deviation of 0.5, what is the standard error of the mean?

Accepted Answer

$$SE = \frac{0.5}{\sqrt{100}} = 0.05$$

Question 15

Which of the following is a discrete probability distribution commonly used in business statistics?

Accepted Answer

Binomial distribution

Question 16

A company wants to estimate the proportion of defective products in a large shipment. Which statistical concept should they use?

Accepted Answer

Sampling distribution of the proportion

Question 17

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 18

A business wants to test if a new training program increases employee productivity. Which statistical method should they use to compare the mean productivity before and after the program?

Accepted Answer

Paired sample hypothesis test for means

Question 19

Which of the following statements about sampling distributions is TRUE?

Accepted Answer

The sampling distribution of the mean becomes approximately normal as the sample size increases, regardless of the population distribution.

OSC 2030: Business Statistics – Syllabus and Course Overview

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