Q: If the probability of rain tomorrow is 0.3, what is the probability that it does NOT rain?

$$P(\text{not rain}) = 1 - 0.3 = 0.7$$

Q: If the probability of flipping heads on a coin is 0.5, what is the probability of flipping heads twice in a row (assuming independence)?

$$P(\text{heads twice}) = 0.5 \times 0.5 = 0.25$$

Question 1

A researcher collects data on the average height of all students in a university. The value calculated from the entire student body is 170 cm. Is this value a statistic or a parameter?

Accepted Answer

It is a parameter because it describes a population.

Question 2

In a study investigating the effects of a new drug, researchers randomly assign patients to either receive the drug or a placebo and then measure their blood pressure. What type of study is this?

Accepted Answer

Designed experiment

Question 3

Which of the following variables is qualitative?

Accepted Answer

Favorite color

Question 4

A variable records the number of cars passing through a toll booth each hour. Is this variable discrete or continuous?

Accepted Answer

Discrete, because it counts whole numbers.

Question 5

A polling organization selects every 10th person from a list of registered voters. What type of sampling is this?

Accepted Answer

Systematic sampling

Question 6

A survey about exercise habits is conducted at a local gym. Which type of bias is most likely present?

Accepted Answer

Sampling bias

Question 7

In an experiment testing fertilizer effectiveness, the individuals are tomato plants, the factor is fertilizer type, the treatments are organic and synthetic fertilizers, and the response variable is plant height. Which is the response variable?

Accepted Answer

Plant height

Question 8

Given the data set: 2, 4, 4, 6, 8. What is the mean?

Accepted Answer

$$\frac{2+4+4+6+8}{5} = 4.8$$

Question 9

A normal distribution has a mean of 100 and a standard deviation of 15. According to the empirical rule, what percentage of data falls within one standard deviation of the mean?

Accepted Answer

Approximately 68%

Question 10

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?

Accepted Answer

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

Question 11

Given the data set: 3, 7, 8, 12, 15, what is the five-number summary?

Accepted Answer

Min: 3, Q1: 7, Median: 8, Q3: 12, Max: 15

Question 12

A scatterplot shows a strong positive linear relationship between hours studied and exam score. The correlation coefficient is closest to:

Accepted Answer

$$r = 0.9$$

Question 13

The least squares regression line for predicting weight (in kg) from height (in cm) is $$y = 0.5x + 10. $$What does the slope represent?

Accepted Answer

For each additional cm in height, weight increases by 0.5 kg.

Question 14

Which of the following is a valid probability model?

Accepted Answer

Probabilities: 0.2, 0.3, 0.5 (sum = 1)

Question 15

If the probability of rain tomorrow is 0.3, what is the probability that it does NOT rain?

Accepted Answer

$$P(	ext{not rain}) = 1 - 0.3 = 0.7$$

Question 16

If the probability of flipping heads on a coin is 0.5, what is the probability of flipping heads twice in a row (assuming independence)?

Accepted Answer

$$P(	ext{heads twice}) = 0.5 	imes 0.5 = 0.25$$

Question 17

A student randomly guesses on a 4-question multiple-choice quiz (each question has 4 options). What is the probability that the student gets at least one question correct?

Accepted Answer

$$1 - (0.75)^4$ = 0.684$$

Question 18

A random sample is taken using a random digit table. Which of the following best describes this sampling method?

Accepted Answer

Simple random sampling

Question 19

A frequency distribution is created for the number of books read by students in a month. If 10 students read 0 books, 20 read 1 book, and 30 read 2 books, what is the relative frequency for students who read 2 books?

Accepted Answer

$$\frac{30}{10+20+30} = \frac{30}{60} = 0.5$$

MATH 1342 Mid-Term Exam Study Guide: Chapters 1-5 (Introductory Statistics)

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