Question 1

A recent study found a strong correlation between the number of movie tickets sold and the number of space missions launched. Which of the following best explains why it is incorrect to conclude that selling more movie tickets causes more space missions?

Accepted Answer

The increase in both variables is likely due to independent societal and technological advancements, not a direct causal link.

Question 2

In a quality control process, battery weights were measured at four time intervals on five different days. The mean weights for each day were: 12.49, 12.40, 12.50, 12.49, and 12.37. What is the average sample mean $\bar{x}$ for these five days?

Accepted Answer

$\bar{x} = 12.45$

Question 3

Given the following ranges for battery weights over five days: 0.04, 0.04, 0.05, 0.05, 0.05, what is the average range $\bar{R}$?

Accepted Answer

$\bar{R} = 0.046$

Question 4

A clinical trial investigated the effectiveness of a cognitive behavioral therapy app and a relaxation music app for insomnia in young adults. Forty-two participants were randomly assigned to one of the two treatments for six weeks. Sleep quality was assessed at the start and end of the study. What are the experimental units and treatments in this experiment?

Accepted Answer

Experimental units: 42 young adults with insomnia; Treatments: cognitive behavioral therapy app and relaxation music app for six weeks

Question 5

Which of the following best describes the concept of confounding variables in the context of the movie tickets and space missions example?

Accepted Answer

A third variable, such as technological advancement, may be influencing both the number of movie tickets sold and the number of space missions.

Question 6

Suppose the control limits for an R-chart are calculated using $LCL_R = D_3 	imes \bar{R}$ and $UCL_R = D_4 	imes \bar{R}$, where $D_3 = 0$ and $D_4 = 2.28$ for a sample size of 4. If $\bar{R} = 0.05$, what are the control limits?

Accepted Answer

$LCL_R = 0.00$, $UCL_R = 0.114$

Question 7

In the insomnia study, why is random assignment of participants to treatments important?

Accepted Answer

It helps ensure that differences in outcomes are due to the treatments and not to pre-existing differences among participants.

Question 8

Which of the following statements about correlation and causation is correct?

Accepted Answer

Correlation does not imply causation; two variables may be correlated due to a third factor.

Question 9

A researcher wants to test if a new app improves sleep quality. Which of the following is the best way to design the experiment?

Accepted Answer

Randomly assign participants to either the new app or a control group and measure sleep quality before and after the intervention.

Question 10

If the range of battery weights on a given day is calculated as the difference between the maximum and minimum values, which formula should be used?

Accepted Answer

$R = \max(x_i) - \min(x_i)$

Question 11

In the context of quality control charts, what does it mean if a data point falls outside the control limits?

Accepted Answer

It suggests that the process may be out of control and requires investigation.

Question 12

Which of the following is a key reason for using a control group in an experiment?

Accepted Answer

To provide a baseline for comparison and help isolate the effect of the treatment.

Question 13

A business analyst observes a correlation coefficient $r = 0.85$ between advertising spending and sales revenue. What does this value indicate?

Accepted Answer

There is a strong positive linear relationship between advertising spending and sales revenue.

Question 14

In an experiment, what is the primary purpose of randomization?

Accepted Answer

To reduce bias and ensure groups are comparable.

Question 15

Which of the following best describes an observational study?

Accepted Answer

Researchers observe and measure variables without assigning treatments.

Question 16

A company wants to monitor the consistency of its product weights. Which statistical tool is most appropriate?

Accepted Answer

Control charts (such as X-bar and R charts)

Question 17

If a process is in statistical control, what does this imply?

Accepted Answer

The process variation is due only to common causes, not special causes.

Question 18

Which formula is used to calculate the sample mean $\bar{x}$ for a set of measurements $x_1, x_2, ..., x_n$?

Accepted Answer

$\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$

Question 19

In the insomnia study, sleep quality was measured at the start and end of the experiment. What type of data collection is this?

Accepted Answer

Pre-test/post-test measurement

Key Concepts in Statistics for Business: Correlation, Control Charts, and Experimental Design

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