Question 1

A researcher wants to study the effect of a new drug on blood pressure. She randomly assigns participants to either receive the drug or a placebo and measures their blood pressure after 4 weeks. Which type of study is this?

Accepted Answer

Experiment

Question 2

Which of the following best describes a parameter?

Accepted Answer

A numerical summary of a population

Question 3

A survey records the number of books each student read last year. Which type of variable is this?

Accepted Answer

Discrete numerical

Question 4

Which graphical display is most appropriate for showing the distribution of a categorical variable such as favorite ice cream flavor?

Accepted Answer

Bar graph

Question 5

A data set of exam scores is strongly right-skewed. Which measure of central tendency is most appropriate to describe the typical score?

Accepted Answer

Median

Question 6

Given the following five-number summary for the ages of patients in a clinic: Min = 18, Q1 = 25, Median = 32, Q3 = 40, Max = 65. What is the interquartile range (IQR)?

$$	ext{IQR} = Q_3$ - Q_1$

Accepted Answer

$$	ext{IQR} = 40 - 25 = 15$$

Question 7

A student scored 85 on a test where the mean was 80 and the standard deviation was 5. What is the student's z-score?

$$z = \frac{x - \mu}{\sigma}$$

Accepted Answer

$$z = \frac{85 - 80}{5} = 1$$

Question 8

In a bell-shaped distribution, approximately what percentage of data falls within two standard deviations of the mean according to the Empirical Rule?

Accepted Answer

95%

Question 9

A boxplot of two groups shows that Group A has a much larger interquartile range (IQR) than Group B. What does this indicate about Group A?

Accepted Answer

Group A has more variability in the middle 50% of its data

Question 10

A probability model assigns $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$P(C) = 0.2. $$What is the sum of the probabilities, and does this model meet the requirements?

$$\sum P(E_i) = 1$$

Accepted Answer

Sum is 1.0; model meets requirements

Question 11

If the probability of rain tomorrow is 0.15, what is the probability that it does NOT rain?

$$P(	ext{not rain}) = 1 - P(	ext{rain})$$

Accepted Answer

$$P(	ext{not rain}) = 0.85$$

Question 12

A fair six-sided die is rolled. What is the probability of rolling a 2 or a 4?

$$P(2 	ext{ or } 4) = P(2) + P(4)$$

Accepted Answer

$$\frac{2}{6}$$

Question 13

In a medical study, 10% of patients experience side effects from a drug. If 5 patients are treated, what is the probability that at least one experiences side effects?

$$P(	ext{at least 1}) = 1 - P(	ext{none})$$

$$P(	ext{none}) = (1 - 0.10)^5$

Accepted Answer

$$1 - (0.90)^5$ \approx 0.41$$

Question 14

Two events, A and B, are independent. If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, what is $$P(A 	ext{ and } B)$$?

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Accepted Answer

$$0.2$$

Question 15

A deck of cards contains 52 cards. What is the probability of drawing a heart or a king?

$$P(	ext{heart or king}) = P(	ext{heart}) + P(	ext{king}) - P(	ext{heart and king})$$

Accepted Answer

$$\frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52}$$

Question 16

In a study, 60% of patients are female. If a patient is randomly selected, what is the probability that the patient is male?

Accepted Answer

0.4

Question 17

A data set has a mean of 50 and a standard deviation of 10. If an outlier of 100 is added, which measure is most affected?

Accepted Answer

Mean

Question 18

A hospital records the time (in minutes) it takes for patients to be seen by a doctor. Which type of variable is this?

Accepted Answer

Continuous numerical

Question 19

A researcher wants to know if eating breakfast is associated with higher test scores. She surveys students about their breakfast habits and test scores. Can she claim a cause-and-effect relationship?

Accepted Answer

No, because this is an observational study

Introductory Statistics: Study Guide for Chapters 1, 2, 3, and 5

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