Question 1

A nutritionist randomly assigns 25 adults to a new diet and 25 adults to continue their usual diet, then measures cholesterol levels after 3 months. In this experiment, what are the subjects and what are the treatments?

Accepted Answer

Subjects: adults; Treatments: new diet and usual diet

Question 2

A marine biologist collects 60 crabs from the Gulf of Mexico to estimate the average length of crabs. In this study, what is the population and what is the sample?

Accepted Answer

Population: all crabs in the Gulf of Mexico; Sample: the 60 crabs collected

Question 3

A nutritionist finds that the average daily sugar intake of 40 randomly selected adults in a city is 25 grams. Which of the following correctly identifies the parameter and the statistic?

Accepted Answer

Parameter: average daily sugar intake of all adults in the city; Statistic: 25 grams (average of the sample)

Question 4

Which of the following is a main benefit of using random sampling in a study?

Accepted Answer

It ensures the sample is representative of the population, reducing selection bias.

Question 5

A nutritionist studies the relationship between hours of exercise per week (X) and blood pressure (Y) in adults. She notices that participants have different daily salt intakes. What is the role of daily salt intake in this study?

Accepted Answer

It is a confounding variable.

Question 6

A researcher gives a vitamin supplement to one group of mice and no supplement to another group, then measures antibody levels after 6 weeks. What type of study is this?

Accepted Answer

An experiment

Question 7

Which statement best describes the Central Limit Theorem?

Accepted Answer

As the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.

Question 8

State the Law of Large Numbers.

Accepted Answer

As the number of trials increases, the sample mean approaches the population mean.

Question 9

Given the following probability distribution for a die: outcomes 1, 2, 3, 4, 5, 6 with probabilities 0.1, 0.2, 0.3, 0.2, ?, 0.1. What is the probability of rolling a 5?

Accepted Answer

$$0.1$$

Question 10

For the same die probability distribution, what is the probability of rolling a 1 or a 3?

Accepted Answer

$$0.4$$

Question 11

Is the random variable X (the die outcome) described above discrete or continuous?

Accepted Answer

Discrete, because it can only take specific integer values.

Question 12

What is the sample space for rolling a die?

Accepted Answer

$$\{1, 2, 3, 4, 5, 6\}$$

Question 13

In a psychology course, the regression equation $$y = 50 - 2x$$ predicts anxiety (y) from hours of daily exercise (x). What is the slope and what does it mean?

Accepted Answer

Slope: $$-2. $$For each additional hour of exercise, anxiety decreases by 2 points.

Question 14

Using the regression equation $$y = 50 - 2x$$, what is the predicted anxiety score for someone who exercises 8 hours per week?

Accepted Answer

$$y = 50 - 2 	imes 8 = 34$$

Question 15

According to a recent study, the heights of adult men in a city are normally distributed with mean $$\mu = 175 cm $$and standard deviation $$\sigma = 10 cm. $$What is the $$z-$$score for a man who is 177 cm tall?

Accepted Answer

$$z = \frac{177 - 175}{10} = 0.2$$

Question 16

Using the normal distribution with $$\mu = 175 cm $$and $$\sigma = 10 cm$$, what is the probability that a randomly selected man is less than 177 cm tall?

Accepted Answer

Approximately $$0.58$$

Question 17

Which of the following best describes a confounding variable in an experiment?

Accepted Answer

A variable that influences both the independent and dependent variables, potentially distorting the results.

Question 18

Which of the following is NOT a benefit of random assignment in experiments?

Accepted Answer

It guarantees the treatment will be effective.

Statistics Exam Study Guide: Sampling, Experiments, Probability, and Regression

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