Statistical Quiz (Business)

In business research, observational studies are sometimes referred to as natural experiments. Explain what this means in the context of market analysis. Choose the correct answer below.

• In an observational study, businesses are assigned to different marketing strategies through random selection.

• In an observational study, a researcher measures characteristics of interest of a part of a market but does not change existing conditions.

• In an observational study, businesses are paired up according to a similarity.

• In an observational study, a marketing strategy is applied to part of a market and responses are observed.

Answer explanation

Observational studies, or natural experiments, involve researchers measuring characteristics of a population without altering conditions. This distinguishes them from experimental studies where treatments are applied.

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Types of marketing strategies. The variable is (1) __________ because strategies are (2) __________.

Answer explanation

The variable is (1) qualitative because places are (2) attributes or labels. They describe characteristics of locations rather than providing numerical values.

Identify the sampling technique used. A marketing firm randomly selected 30 of the nation's shopping malls and surveyed all of the store managers at each mall.

• random

• stratified

• convenience

• cluster

• systematic

Answer explanation

The researcher used a cluster sampling technique by randomly selecting 30 middle schools (clusters) and interviewing all teachers within those selected schools, rather than sampling individual teachers across all schools.

The quarterly sales figures (in millions) for 10 different products are listed below. Find the range of the data set. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

• 2.8

• 3.2

• 1.4

• 2.45

Answer explanation

To find the range, subtract the minimum value (0.8) from the maximum value (4.0). Thus, 4.0 - 0.8 = 3.2. However, the range is often expressed as the difference between the highest and lowest values, which is 1.4.

In a marketing campaign, the average number of leads generated per day is 56 with a standard deviation of 4. On a particular day, the team generated 64 leads. Find the z-score for this day's performance.

• z = 1.07

• z = 2.00

• z = -1.07

• z = 1.75

Answer explanation

To find the z-score, use the formula z = (X - μ) / σ. Here, X = 64, μ = 56, and σ = 4. Thus, z = (64 - 56) / 4 = 8 / 4 = 2.00. Therefore, the correct answer is z = 2.00.

In a marketing campaign, a company wants to choose 4 out of 7 different advertising strategies to implement. Determine whether the statement below is true or false. If it is false, rewrite it as a true statement. Choose the correct answer below.

• This statement is false. A true statement is 7C4 = 7C2.

• This statement is false. A true statement is 2C7 = 5C7.

• This statement is false. A true statement is 7C5 = 7P2.

• This statement is true.

Answer explanation

The statement is false because 7C5 does equal 7P2. The correct relationship is that combinations can be expressed in terms of permutations, specifically nCr = nPr / r!.

Identify the two events described in the study and determine if the results indicate that the events are independent or dependent. Explain your reasoning. A study found that there is no relationship between advertising on social media and an increase in product sales. Identify the two events. Choose the correct answer below.

• Increasing product sales and not increasing product sales.

• Advertising on social media and being around people who buy the product.

• Advertising on social media and increasing product sales.

• Advertising on social media and not advertising on social media.

Answer explanation

The two events are being around satellite televisions and developing cancer. The study indicates no relationship between these events, suggesting they are independent, as one does not affect the likelihood of the other.

Are the marketing strategies independent or dependent?

• Independent. The success of a product is related to the number of advertisements aired.

• Independent. The number of advertisements aired does not directly cause the success of a product.

• Dependent. The number of advertisements aired does cause the success of a product.

• Dependent. The success of a product is caused by one's exposure to advertisements.

Answer explanation

The correct choice is 'Independent. Being around satellite televisions does not cause cancer.' This indicates that the events are not related, as exposure to satellite televisions does not influence cancer development.

What is the capital of France?

Answer explanation

The probability that an event will not happen is calculated as 1 - P(E). Here, P(E) = 0.24, so the probability that the event will not happen is 1 - 0.24 = 0.76.

Explain why the statement is incorrect. The probability of a marketing campaign's success is 148%. What makes the statement incorrect?

• The probability of an event must be contained in the interval [1,100].

• The probability of an event cannot exceed 100%.

• An event needs to have more than one possible outcome.

• The chance of a campaign's success is always more than 100%.

Answer explanation

The statement is incorrect because the probability of an event cannot exceed 100%. Probabilities are expressed as values between 0% and 100%, where 100% indicates certainty of the event occurring.