Question 1

Which of the following best describes the difference between a population and a sample in statistics?

Accepted Answer

A sample is a subset of a population, used to make inferences about the population.

Question 2

A pharmaceutical company wants to estimate the average recovery time for a new drug. They select 100 patients from a hospital and record their recovery times. Which of the following is the sample statistic?

Accepted Answer

The average recovery time of the 100 selected patients.

Question 3

Which of the following graphical methods is most appropriate for displaying the distribution of a single quantitative variable?

Accepted Answer

Histogram

Question 4

Given the following data set representing the number of hours studied by 7 students: 2, 4, 4, 5, 6, 8, 10. What is the median?

Accepted Answer

$$5$$

Question 5

A researcher collects the following data: 3, 7, 7, 7, 10. What is the mode of the data set?

Accepted Answer

$$7$$

Question 6

Which of the following is the correct formula for the sample variance $$s^2 of$$ $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$s^2$$ = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x}$$)^2$$

Question 7

A boxplot is most useful for which of the following purposes?

Accepted Answer

Showing the distribution, center, spread, and potential outliers of a quantitative variable.

Question 8

If the mean of a data set is $$50$$ and the standard deviation is $$5$$, what is the z-score of a value $$x = 60$$?

Accepted Answer

$$z = 2$$

Question 9

A fair six-sided die is rolled twice. What is the probability that both rolls result in a 6?

Accepted Answer

$$\frac{1}{36}$$

Question 10

Which of the following is the correct formula for the binomial probability of getting exactly $$k$$ successes in $$n$$ independent trials, each with probability $$p of $$success?

Accepted Answer

$$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$

Question 11

A multiple-choice test has 5 questions, each with 4 possible answers (only one correct). If a student guesses on all questions, what is the probability they get exactly 2 correct answers?

Accepted Answer

$$P = \binom{5}{2} (0.25)^2$ (0.75)^3$

Question 12

Which of the following statements about the Central Limit Theorem is correct?

Accepted Answer

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

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

$$2$$

Question 14

Which of the following is the correct formula for a 95% confidence interval for a population mean $$\mu$$ when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$$

Question 15

A researcher wants to test if the mean weight of a certain species of fish is different from 10 kg. Which type of hypothesis test should be used?

Accepted Answer

A two-tailed test for the population mean.

Question 16

Which of the following best describes the meaning of a p-value in hypothesis testing?

Accepted Answer

The probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true.

Question 17

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. Which of the following is the best interpretation?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam scores.

Question 18

Which of the following is the correct formula for the regression line predicting $$y$$ from $$x$$?

Accepted Answer

$$\hat{y} = b_0$ + b_1$ x$$

Question 19

A hospital administrator wants to estimate the proportion of patients who recover within 3 days after surgery. Which type of data and statistical method should be used?

Accepted Answer

Categorical data; estimation of a population proportion.

Question 20

A sample of 25 batteries has a mean lifetime of 100 hours and a standard deviation of 10 hours. What is the 95% confidence interval for the mean battery lifetime? (Assume normality and use $$t^* = 2.064$$ for 24 degrees of freedom.)

Accepted Answer

$$100 \pm 2.064 	imes \frac{10}{\sqrt{25}}$$

Statistics Course Study Guide: Key Topics and Concepts

Guida di studio - Domande di pratica

Study guide - Flashcard