Question 1

A pharmaceutical company wants to test whether a new drug lowers blood pressure more effectively than the current standard. They randomly assign 100 patients to receive either the new drug or the standard drug and compare the average reduction in blood pressure. What type of study is this?

Accepted Answer

An experimental study

Question 2

Which of the following best describes a population parameter?

Accepted Answer

A numerical characteristic of a population

Question 3

A researcher collects data on the number of books read by students in a month. Which type of variable is this?

Accepted Answer

Quantitative discrete

Question 4

Which of the following is NOT a property of the mean?

Accepted Answer

It is always the most frequently occurring value in a dataset

Question 5

Given the following data set: 2, 4, 4, 6, 8, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 6 - 4 = 2$$

Question 6

A boxplot is constructed for the weights of apples in a shipment. If a value is greater than $$Q_3 + 1.5$$ 	imes IQR$$, how is it classified?

Accepted Answer

As an upper outlier

Question 7

A survey records the favorite color of 200 students. Which type of data is this?

Accepted Answer

Nominal

Question 8

If the probability of event A is 0.3 and the probability of event B is 0.5, and A and B are independent, what is the probability that both A and B occur?

Accepted Answer

$$P(A \cap B) = 0.15$$

Question 9

A fair die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

$$P = \frac{2}{6} = \frac{1}{3}$$

Question 10

Which of the following is a property of a probability distribution for a discrete random variable?

Accepted Answer

The sum of all probabilities must be 1

Question 11

A binomial experiment consists of 5 trials with probability of success $$p = 0.4. $$What is the probability of exactly 2 successes? (Use the binomial formula: $$P(X = k) = \frac{n!}{k!(n-k)!} p^k (1-p$$)^{n-k}$$)

Accepted Answer

$$P(X=2) = 0.3456$$

Question 12

Which of the following statements about the normal distribution is TRUE?

Accepted Answer

About 68% of the data falls within 1 standard deviation of the mean

Question 13

A sample of 36 students has a mean test score of 80 and a standard deviation of 12. What is the standard error of the mean?

Accepted Answer

$$SE = \frac{12}{\sqrt{36}} = 2$$

Question 14

Which of the following will result in a narrower confidence interval for the mean, assuming all other factors are held constant?

Accepted Answer

Decreasing the standard deviation

Question 15

A researcher wants to estimate the mean height of adult males in a city. She collects a random sample and constructs a 95% confidence interval. Which of the following is the correct interpretation?

Accepted Answer

We are 95% confident that the interval contains the true population mean

Question 16

Which of the following is a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis

Question 17

Suppose the null hypothesis is $$H_0$$: \mu = 50$$ and the alternative is H_a$$: \mu \u003e 50$$. If the p-value is 0.03 and $$\alpha = 0.05$$, what is the correct decision?

Accepted Answer

Reject $$H_0$$

Question 18

A z-score is calculated as $$z = \frac{x - \mu}{\sigma}. $$What does a z-score of 2.5 indicate?

Accepted Answer

The value is 2.5 standard deviations above the mean

Question 19

Which of the following is NOT a requirement for a binomial experiment?

Accepted Answer

The probability of success changes from trial to trial

Question 20

According to the Central Limit Theorem, as the sample size increases, the sampling distribution of the sample mean:

Accepted Answer

Approaches a normal distribution

Statistics Study Guide: Key Concepts and Methods

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