Q: A researcher wants to estimate the average number of hours employees work per week at a large corporation. She collects a random sample of 50 employees and calculates a sample mean of 42 hours with a sample standard deviation of 5 hours. What is the 95% confidence interval for the population mean?

$$42 \pm 1.96 \times \frac{5}{\sqrt{50}}$$

Q: A business analyst is testing whether the average transaction value at a store is different from $50. She collects a sample and performs a two-tailed hypothesis test. Which of the following is the correct formulation of the null and alternative hypotheses?

$$H_0$$: \mu = 50$$, H_a$$: \mu \neq 50$$

Question 1

A business manager wants to summarize the monthly sales data for her team. Which of the following statistical measures would best describe the central tendency of the sales data?

Accepted Answer

The mean, because it provides the arithmetic average of all sales values.

Question 2

A company is analyzing the time it takes to deliver products to customers. The delivery times are normally distributed with a mean of 5 days and a standard deviation of 1 day. What is the probability that a randomly selected delivery will take more than 7 days? Use the standard normal distribution.

Accepted Answer

$$P(X \u003e 7) = P(Z \u003e \frac{7-5}{1}) = P(Z \u003e 2) = 0.0228$$

Question 3

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

Accepted Answer

To determine if there is enough evidence to support a specific claim about a population parameter.

Question 4

A researcher wants to estimate the average number of hours employees work per week at a large corporation. She collects a random sample of 50 employees and calculates a sample mean of 42 hours with a sample standard deviation of 5 hours. What is the 95% confidence interval for the population mean?

Accepted Answer

$$42 \pm 1.96 	imes \frac{5}{\sqrt{50}}$$

Question 5

In regression analysis, what does the coefficient of determination ($$R^2) $$indicate?

Accepted Answer

The proportion of the total variation in the dependent variable explained by the independent variable(s).

Question 6

A business analyst is testing whether the average transaction value at a store is different from $50. She collects a sample and performs a two-tailed hypothesis test. Which of the following is the correct formulation of the null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu = 50$$, H_a$$: \mu 
eq 50$$

Question 7

A company wants to know if a new training program improves employee productivity. They measure productivity before and after the program for a random sample of employees. Which statistical test should they use?

Accepted Answer

Paired sample t-test

Question 8

Which of the following is NOT an assumption of the simple linear regression model?

Accepted Answer

The dependent variable must be categorical.

Question 9

A sample of 100 customers is surveyed to determine if there is a relationship between age group (under 30, 30-50, over 50) and product preference (A, B, C). Which statistical test is most appropriate?

Accepted Answer

Chi-square test for independence

Question 10

A manufacturer claims that less than 5% of its products are defective. In a random sample of 200 products, 8 are found to be defective. What is the sample proportion of defective products?

Accepted Answer

$$\frac{8}{200} = 0.04$$

Question 11

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

Accepted Answer

Descriptive statistics summarize data; inferential statistics use data to make predictions or generalizations about a population.

Question 12

A business wants to estimate the proportion of customers who are satisfied with their service. In a random sample of 400 customers, 320 report being satisfied. Construct a 95% confidence interval for the population proportion.

Accepted Answer

$$\hat{p} \pm 1.96 \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$, where $$\hat{p} = \frac{320}{400} = 0.8$$

Question 13

A manager wants to compare the average sales of three different stores. Which statistical method should be used?

Accepted Answer

One-way ANOVA

Question 14

If the probability of a customer making a purchase on any given day is 0.2, what is the probability that exactly 3 out of 10 customers make a purchase? (Assume a binomial distribution.)

Accepted Answer

$$P(X=3) = {10 \choose 3} (0.2)^3$ (0.8)^7$

Question 15

Which of the following is a correct interpretation of a p-value in hypothesis testing?

Accepted Answer

The probability of observing the sample data, or something more extreme, if the null hypothesis is true.

Question 16

A business analyst uses a sample to estimate the population mean. Which formula is used to calculate the standard error of the mean?

Accepted Answer

$$SE = \frac{s}{\sqrt{n}}$$

Question 17

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

Accepted Answer

Simple linear regression

Question 18

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

Accepted Answer

Rejecting the null hypothesis when it is actually true.

Question 19

A business collects data on the number of products sold each day for a month. Which type of variable is 'number of products sold'?

Accepted Answer

Quantitative discrete variable

Business Statistics: Core Concepts and Applications

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