Q: A diagnostic test for a disease yields the following results: 40 true positives, 10 false positives, 50 true negatives, and 5 false negatives. What is the probability that a randomly selected person who tested positive actually has the disease?

$$P(\text{Disease} | \text{Positive}) = \frac{40}{40+10} = \frac{40}{50} = 0.8$$

Q: A student randomly guesses on a 4-question multiple-choice quiz (each question has 5 choices). What is the probability they get at least one question correct?

$$P(\text{at least one correct}) = 1 - (0.8)^4$ = 1 - 0.4096 = 0.5904$$

Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical measurement describing a population, while a statistic describes a sample.

Question 2

A pharmaceutical company claims their new drug reduces blood pressure by an average of 1 mmHg. A large clinical trial finds this result is statistically significant (p \u003c 0.05). Which statement best explains why this result may lack practical significance?

Accepted Answer

Practical significance considers whether the effect size is meaningful in real life, and 1 mmHg may not be clinically important.

Question 3

Which level of measurement is most appropriate for the following variable: 'Temperature measured in degrees Celsius'?

Accepted Answer

Interval

Question 4

A researcher wants to compare the variability of two datasets: one measuring heights (in cm) and one measuring weights (in kg). Which statistic should they use?

Accepted Answer

Coefficient of variation $$\mathrm{CV} = \frac{s}{\overline{x}} 	imes 100\%$$

Question 5

Given the data set: 8, 12, 15, 15, 20, 22, 30, what is the sample mean $$\overline{x}$$?

Accepted Answer

$$\overline{x} = \frac{8+12+15+15+20+22+30}{7} = \frac{122}{7} \approx 17.43$$

Question 6

A histogram is most appropriate for which type of data?

Accepted Answer

Quantitative data, to show shape and detect outliers

Question 7

A student scores 85 on a test where the class mean is 75 and the standard deviation is 5. What is the student's z-score?

Accepted Answer

$$z = \frac{85 - 75}{5} = 2$$

Question 8

Which of the following is NOT a potential source of bias in a survey?

Accepted Answer

Using a random sample

Question 9

In a boxplot, which values are used to determine the 'fences' for identifying outliers?

Accepted Answer

Q1, Q3, and the interquartile range (IQR)

Question 10

A frequency distribution has classes: 0–9, 10–19, 20–29. What are the class boundaries for the first class?

Accepted Answer

0.5 and 9.5

Question 11

A diagnostic test for a disease yields the following results: 40 true positives, 10 false positives, 50 true negatives, and 5 false negatives. What is the probability that a randomly selected person who tested positive actually has the disease?

Accepted Answer

$$P(	ext{Disease} | 	ext{Positive}) = \frac{40}{40+10} = \frac{40}{50} = 0.8$$

Question 12

If two events A and B are independent, which formula correctly gives the probability that both occur?

Accepted Answer

$$P(A \cap B) = P(A) \cdot P(B)$$

Question 13

A student randomly guesses on a 4-question multiple-choice quiz (each question has 5 choices). What is the probability they get at least one question correct?

Accepted Answer

$$P(	ext{at least one correct}) = 1 - (0.8)^4$ = 1 - 0.4096 = 0.5904$$

Question 14

Which formula is used to calculate the sample standard deviation $$s$$?

Accepted Answer

$$s = \sqrt{ \frac{ \sum (x - \overline{x})^2$ }{ n - 1 } }$$

Question 15

A dataset has minimum value 5 and maximum value 25. What is the midrange?

Accepted Answer

$$MR = \frac{5 + 25}{2} = 15$$

Question 16

Which of the following best describes a confounding variable?

Accepted Answer

A variable that is related to both the explanatory and response variables and can distort their relationship.

Question 17

How many ways can 3 students be arranged in a line?

Accepted Answer

$$P(3,3) = 3! = 6$$

Question 18

A scatterplot shows points trending upward as x increases. What type of association is this?

Accepted Answer

Positive association

Question 19

Which formula gives the probability of the union of two events A and B?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Elementary Statistics Exam 1 Study Guide: Chapters 1–4 (Triola)

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