Q: A pharmaceutical company tests a new drug and finds the mean recovery time is 8 days with a standard deviation of 2 days. If a random sample of 25 patients is taken, what is the standard error of the mean?

$$\text{Standard Error} = \frac{2}{\sqrt{25}} = 0.4$$

Q: Which formula represents the probability of two independent events A and B both occurring?

$$P(A \text{ and } B) = P(A) \times P(B)$$

Q: A random variable $$X$$ follows a binomial distribution with $$n = 10$$ and $$p = 0.5. $$What is the expected value $$E[X]$$?

$$E[X] = n \times p = 10 \times 0.5 = 5$$

Question 1

Which of the following best describes the purpose of a confidence interval in business statistics?

Accepted Answer

To provide a range of plausible values for a population parameter based on sample data.

Question 2

A company wants to understand the relationship between advertising spending and sales revenue. Which statistical method should they use?

Accepted Answer

Simple linear regression

Question 3

In a survey, 60 out of 200 customers prefer a new product. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{60}{200} = 0.3$$

Question 4

Which of the following is a key assumption when using the normal distribution to model continuous random variables?

Accepted Answer

The data are independent and identically distributed.

Question 5

A pharmaceutical company tests a new drug and finds the mean recovery time is 8 days with a standard deviation of 2 days. If a random sample of 25 patients is taken, what is the standard error of the mean?

Accepted Answer

$$	ext{Standard Error} = \frac{2}{\sqrt{25}} = 0.4$$

Question 6

Which formula represents the probability of two independent events A and B both occurring?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Question 7

A business analyst uses a two-way table to study the relationship between gender and product preference. What type of data is being analyzed?

Accepted Answer

Categorical data

Question 8

Which of the following is NOT a valid method for collecting data in business statistics?

Accepted Answer

Guessing

Question 9

A retailer wants to estimate the proportion of customers who use their loyalty program. Which formula should they use to construct a 95% confidence interval for the proportion?

Accepted Answer

$$\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 10

Which statement best describes the ethical implications of using statistics in business?

Accepted Answer

Statistical methods must be applied honestly and transparently to avoid misleading stakeholders.

Question 11

A bank wants to test if the mean loan approval time is less than 3 days. Which hypothesis test should they use if the population standard deviation is known?

Accepted Answer

Z-test for population mean

Question 12

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 13

A random variable $$X$$ follows a binomial distribution with $$n = 10$$ and $$p = 0.5. $$What is the expected value $$E[X]$$?

Accepted Answer

$$E[X] = n 	imes p = 10 	imes 0.5 = 5$$

Question 14

Which formula represents the simple linear regression equation?

Accepted Answer

$$y = \$$beta_0$$ + \$$beta_1$$ x$$

Question 15

A manufacturer wants to know if the proportion of defective products is greater than 5%. Which statistical test should they use?

Accepted Answer

One-sample z-test for proportion

Question 16

Which formula is used to calculate the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \frac{\sum x_i}{n}$$

Question 17

A business collects data on customer satisfaction scores (1-10). Which type of variable is this?

Accepted Answer

Discrete random variable

Question 18

If $$P(A) = 0.4$$ and $$P(B \mid A) = 0.5$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B \mid A) = 0.4 	imes 0.5 = 0.2$$

Question 19

A company wants to visualize the distribution of sales revenue. Which graphical method is most appropriate?

Accepted Answer

Histogram

Question 20

Which formula is used to calculate the standard deviation $$s of a $$sample?

Accepted Answer

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

Statistics for Business Sciences: Course Syllabus and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard