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

Given the following sample means for notebook battery weights over five days: $$12.49, 12.40, 12.49, 12.49, 12.37$$, compute the average sample mean $$\bar{x}.$$

Accepted Answer

$$\bar{x} = 12.45$$

Question 3

In a quality control process, the average range $$\bar{R} of $$battery weights over five days is $$0.05. If $$the lower control limit for the R-chart is $$LCL_R = 0.00$$ and the upper control limit is $$UCL_R = 0.114$$, which of the following statements is correct?

Accepted Answer

The process is in control because $$0.05 is $$between $$0.00$$ and $$0.114.$$

Question 4

A clinical trial investigated the effectiveness of a new cognitive behavioral therapy app for reducing symptoms of insomnia in young adults. Forty-two participants aged 20 to 22 with chronic insomnia were randomly assigned to use either the cognitive behavioral therapy app or a relaxation music app for six weeks. Sleep quality was assessed at the start and end of the study. What are the experimental units and the 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 difference between correlation and causation?

Accepted Answer

Correlation means two variables move together, but causation means one variable directly affects the other.

Question 6

Suppose a researcher finds a strong positive correlation between ice cream sales and drowning incidents. Which of the following is the most likely explanation?

Accepted Answer

A lurking variable, such as temperature, increases both ice cream sales and swimming activity, leading to more drownings.

Question 7

In an experiment, what is the primary purpose of random assignment of subjects to treatments?

Accepted Answer

To reduce the impact of confounding variables and ensure groups are comparable.

Question 8

A quality control engineer calculates the control limits for an R-chart as $$LCL_R = 0.00$$ and $$UCL_R = 0.114. If a $$new sample has a range of $$0.12$$, what should the engineer conclude?

Accepted Answer

The process may be out of control since $$0.12 is $$close to $$UCL_R$$ but still within limits.

Question 9

Which of the following is an example of a confounding variable in an experiment studying the effect of a new drug on blood pressure?

Accepted Answer

Participants' diet, if not controlled, could affect blood pressure independently of the drug.

Question 10

A researcher wants to test whether a new teaching method improves student test scores. Which of the following would be the best experimental design?

Accepted Answer

Randomly assign students to either the new method or the traditional method, then compare test scores.

Question 11

If the mean of a data set is $$\mu = 50$$ and the standard deviation is $$\sigma = 5$$, what is the z-score for a value of $$60$$?

Accepted Answer

$$z = 2$$

Question 12

In a clinical trial, what is the main reason for using a control group?

Accepted Answer

To provide a baseline for comparison to determine the effect of the treatment.

Question 13

Which of the following statements about experimental units and treatments is correct?

Accepted Answer

Experimental units are the subjects or objects to which treatments are applied.

Question 14

A study finds a correlation coefficient of $$r = 0.95$$ between two variables. Which of the following is the best interpretation?

Accepted Answer

There is a strong linear relationship between the two variables.

Question 15

If the average range $$\bar{R}$$ for a process is $$0.05$$ and the control limits are $$LCL_R = 0.00$$ and $$UCL_R = 0.114$$, what does it mean if a future sample has a range of $$0.15$$?

Accepted Answer

The process is out of control because $$0.15 is $$above $$UCL_R.$$

Question 16

Which of the following is NOT a valid reason for using control charts in quality control?

Accepted Answer

To guarantee that all products will be defect-free.

Question 17

A study finds a correlation between the number of hours studied and exam scores. Which of the following would be the best way to test if studying more causes higher exam scores?

Accepted Answer

Conduct an experiment where students are randomly assigned to different study durations and compare their exam scores.

Key Concepts in Statistical Reasoning, Control Charts, and Experimental Design

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