Question 1

A nutritionist wants to study the effect of a new diet plan on cholesterol levels. She selects 50 adults and randomly assigns 25 to follow the new diet, while the other 25 continue their usual diet. After 3 months, she measures the cholesterol levels of all participants. What is the treatment in this study?

Accepted Answer

The new diet plan assigned to half the participants

Question 2

A marine biologist wants to estimate the average length of crabs in the Gulf of Mexico. She collects 60 crabs and finds that their average daily length is 25 cm. What is the sample in this study?

Accepted Answer

The 60 crabs collected by the biologist

Question 3

A nutritionist wants to know the average daily sugar intake of adults in a city. She randomly selects 40 adults and finds that their average daily sugar intake is 25 grams. What is the population in this study?

Accepted Answer

All adults in the city

Question 4

Which of the following best describes the parameter in the previous question about sugar intake?

Accepted Answer

The average daily sugar intake of all adults in the city

Question 5

A nutritionist studies the relationship between the number of hours of sound sleep per week ($$X) $$and blood pressure levels ($$Y). $$She finds that adults who exercise more have higher blood pressure. What is the explanatory variable in this study?

Accepted Answer

Number of hours of sound sleep per week ($$X)$$

Question 6

A researcher wants to test the effect of a new vitamin supplement on the cholesterol levels of mice. She gives the supplement to one group of mice and gives no supplement to another group. After 6 weeks, she measures the antibody levels in all mice. What type of study is this?

Accepted Answer

Experimental study

Question 7

Which of the following is a discrete random variable?

Accepted Answer

The number of heads in 10 coin tosses

Question 8

Suppose we have a die that gives the outcomes 1 through 6. What is the probability of rolling a 5?

Accepted Answer

$$\frac{1}{6}$$

Question 9

Which of the following best describes the central limit theorem?

Accepted Answer

The sampling distribution of the sample mean approaches a normal distribution as the sample size increases

Question 10

A researcher collects data on the number of books read by students in a semester: 0, 1, 2, 3, 4, 5. Which of the following is the correct formula for the mean ($$\mu) of $$this data set?

Accepted Answer

$$\mu = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 11

Which of the following is the correct formula for the variance ($$\$$sigma^2$$) of a population?

Accepted Answer

$$\$$sigma^2$$ = \frac{\sum_{i=1}^{n} (x_i - \mu)^2$}{n}$$

Question 12

A linear regression equation was computed to predict the level of anxiety ($$Y) $$from the number of hours of daily exercise ($$X$$): $$Y = 10 - 2X. $$What is the interpretation of the slope in this equation?

Accepted Answer

For each additional hour of exercise, anxiety decreases by 2 units

Question 13

Which of the following is a continuous random variable?

Accepted Answer

The time it takes to run a marathon

Question 14

A researcher wants to know if there is a relationship between the amount of time spent studying and exam scores. Which statistical method is most appropriate?

Accepted Answer

Linear regression

Question 15

Suppose the probability distribution for a random variable $$X is $$given by $$P(X = x) = 0.1$$ for $$x = 0, 1, 2, 3, 4, 5, 6, 7. $$What is the probability that $$X is $$greater than 5?

Accepted Answer

$$0.2$$

Question 16

Which of the following statements about random sampling is correct?

Accepted Answer

Random sampling gives every member of the population an equal chance of being selected

Question 17

A researcher wants to compare the mean blood pressure of two groups: one that exercises regularly and one that does not. Which statistical test should she use?

Accepted Answer

Independent samples t-test

Question 18

Which of the following is the correct formula for the least-squares regression line?

Accepted Answer

$$y = a + bx$$

Question 19

If the mean of a data set is 10 and the standard deviation is 2, what is the z-score for a value of 14?

Accepted Answer

$$z = 2$$

Question 20

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

Accepted Answer

A parameter describes a population, while a statistic describes a sample

Statistics Study Guide: Experimental Design, Data Types, Probability, and Regression

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