Question 1

Which of the following best describes the difference between an experiment and an observational study?

Accepted Answer

An experiment involves manipulating one or more variables to observe the effect on a response variable, while an observational study only observes and measures variables without intervention.

Question 2

A clinical trial is testing a new medication. What is the purpose of including a placebo group?

Accepted Answer

To serve as a baseline for comparison and control for the placebo effect.

Question 3

Which of the following variables is quantitative?

Accepted Answer

The number of cars owned by a family.

Question 4

Suppose the median of a data set is 50, the interquartile range (IQR) is 20, and the data set contains several values above 100. What can you conclude?

Accepted Answer

There are outliers in the data set.

Question 5

A researcher collects the following data: $$X = [2, 4, 6, 8, 10]. $$What is the standard deviation of $$X$$?

Accepted Answer

$$\sqrt{10}$$

Question 6

In a study, the regression equation for predicting exam score ($$y) $$from study time ($$x) is$$ $$y = 50 + 5x. $$What is the predicted exam score for a student who studies for 6 hours?

Accepted Answer

$$y = 50 + 5 	imes 6 = 80$$

Question 7

A light bulb company claims its new LED bulbs last more than 10,000 hours. A sample of 30 bulbs has a mean lifespan of 10,200 hours and a standard deviation of 420 hours. Which hypothesis test should be used to evaluate the company's claim?

Accepted Answer

A one-sample $$t-$$test for the mean.

Question 8

In a university, 600 students are enrolled in both biology and chemistry. 100 got an A in biology, 95 got an A in chemistry, and 50 got an A in both. What is the probability that a randomly chosen student got an A in biology or chemistry?

Accepted Answer

$$P(A \cup B) = \frac{100 + 95 - 50}{600} = \frac{145}{600}$$

Question 9

Which of the following statements about standard deviation is TRUE?

Accepted Answer

If all data values are exactly the same, the standard deviation is zero.

Question 10

A researcher wants to know if there is a statistically significant difference between the mean heights of plants treated with two different fertilizers. Which statistical test should be used?

Accepted Answer

A two-sample $$t-$$test for means.

Question 11

If the correlation coefficient $$r$$ between two variables is $$-0.85$$, what does this indicate?

Accepted Answer

There is a strong negative linear relationship between the variables.

Question 12

Which of the following is NOT a requirement for a valid regression prediction?

Accepted Answer

The sample size must be less than 10.

Question 13

A sample of 50 students has a mean test score of 78 with a standard deviation of 10. What is the 95% confidence interval for the mean score?

Accepted Answer

$$78 \pm 1.96 	imes \frac{10}{\sqrt{50}}$$

Question 14

Which of the following statements is FALSE?

Accepted Answer

If the correlation coefficient is close to zero, there is no relationship between the variables under study.

Question 15

A researcher is interested in the mean salary for software engineers with a bachelor's degree. A random sample of 64 engineers has a mean salary of $$92,000 and a standard deviation of 8$$,000. What is the 99% confidence interval for the mean salary?

Accepted Answer

$$92,000 \pm 2.576 	imes \frac{8,000}{8}$$

Question 16

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The difference between the third quartile ($$Q_3) $$and the first quartile ($$Q_1$$): $$IQR = Q_3$ - Q_1$

Statistics Study Guide: Key Concepts, Problem Types, and Applications

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