Q: A random variable $$X$$ follows a binomial distribution with $$n = 10$$ and $$p = 0.2. $$What is the expected value $$E[X]$$?

$$E[X] = np = 10 \times 0.2 = 2$$

Question 1

Which of the following best describes the Central Limit Theorem (CLT) and its importance in business statistics?

Accepted Answer

The CLT states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.

Question 2

A business analyst uses Excel to create a histogram of monthly sales data. What is the primary purpose of this graphical display?

Accepted Answer

To display the frequency distribution of a single quantitative variable.

Question 3

A company wants to estimate the average time (in minutes) customers spend on their website. They collect a random sample of 100 customers and find a sample mean of 12 minutes with a sample standard deviation of 4 minutes. Construct a 95% confidence interval for the population mean. Which formula should be used?

Accepted Answer

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

Question 4

Which of the following is an example of a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 5

A marketing manager wants to test if a new advertisement increases sales. The null hypothesis is that the mean sales remain unchanged. After collecting data, the p-value is 0.03. If the significance level is 0.05, what should the manager conclude?

Accepted Answer

Reject the null hypothesis; there is evidence that the ad increases sales.

Question 6

Which Excel function would you use to calculate the sample mean of a dataset in a business statistics context?

Accepted Answer

AVERAGE()

Question 7

A company is interested in the proportion of defective products in a large shipment. They sample 200 products and find 10 are defective. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\frac{10}{200} = 0.05$$

Question 8

Which of the following statements about correlation is TRUE?

Accepted Answer

A correlation coefficient of $$r = 1$$ means there is a perfect positive linear relationship.

Question 9

In a simple linear regression model, which equation best represents the relationship between the dependent variable $$y$$ and independent variable $$x$$?

Accepted Answer

$$y = a + bx$$

Question 10

A business wants to test if the average delivery time is less than 3 days. Which of the following is the correct set of hypotheses for this one-sided test?

Accepted Answer

$$H_0$$: \mu = 3$$; H_a$$: \mu \u003c 3$$

Question 11

Which of the following is NOT an ethical issue in statistical practice?

Accepted Answer

Using random sampling methods.

Question 12

A random variable $$X$$ follows a binomial distribution with $$n = 10$$ and $$p = 0.2. $$What is the expected value $$E[X]$$?

Accepted Answer

$$E[X] = np = 10 	imes 0.2 = 2$$

Question 13

Which of the following best describes a p-value in hypothesis testing?

Accepted Answer

The probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true.

Question 14

A sample of 25 business students has a mean test score of 80 and a sample standard deviation of 10. What is the standard error of the mean?

Accepted Answer

$$\frac{10}{\sqrt{25}} = 2$$

Question 15

Which of the following is a correct interpretation of a 95% confidence interval for a population mean?

Accepted Answer

If we took many samples and built a confidence interval from each, about 95% of those intervals would contain the true population mean.

Question 16

A business collects data on the number of hours employees work per week. Which measure would best describe the variability in this data?

Accepted Answer

Standard deviation

Question 17

A researcher is interested in the relationship between advertising budget ($$x) $$and sales revenue ($$y). $$The regression output gives a slope coefficient $$b = 2.5. $$What does this mean?

Accepted Answer

For each additional dollar spent on advertising, sales revenue increases by $$2.5.$$

Question 18

Which of the following is a discrete random variable?

Accepted Answer

The number of defective items in a shipment.

Question 19

A company wants to estimate the proportion of customers who prefer a new product. Which formula should be used to construct a large-sample confidence interval for the population proportion $$p$$?

Accepted Answer

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

Question 20

Which of the following is a potential effect of confounding variables in a business study?

Accepted Answer

They can obscure the true relationship between the variables of interest.

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