Question 1

Which of the following 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 2

A researcher wants to estimate the mean number of hours students study per week. She collects a random sample of 36 students and finds a sample mean of 15 hours with a population standard deviation of 6 hours. Construct a 95% confidence interval for the population mean. Which formula should she use for the margin of error?

Accepted Answer

$$E = z_c \frac{\sigma}{\sqrt{n}}$$

Question 3

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

Accepted Answer

Each trial has more than two possible outcomes.

Question 4

Given a normal distribution with mean $$\mu = 100$$ and standard deviation $$\sigma = 15$$, what is the z-score for a value of $$x = 130$$?

Accepted Answer

$$z = \frac{130 - 100}{15} = 2$$

Question 5

A company claims their mean delivery time is less than 30 minutes. A random sample of 36 deliveries has a mean of 28.5 minutes and a known population standard deviation of 3.5 minutes. What is the appropriate test statistic for testing the company's claim at $$\alpha = 0.01$$?

Accepted Answer

$$z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$$

Question 6

Which of the following sampling methods is most likely to introduce bias?

Accepted Answer

Convenience sampling

Question 7

If the probability of a successful surgery is 0.85, what is the probability that all three surgeries are successful, assuming independence?

Accepted Answer

$$0.85^3$$

Question 8

Which of the following best describes the difference between a permutation and a combination?

Accepted Answer

A permutation considers order, while a combination does not.

Question 9

A frequency distribution is constructed for a data set. What is the range of the data if the lowest value is 12 and the highest value is 47?

Accepted Answer

$$47 - 12 = 35$$

Question 10

Which of the following is a property of the standard normal distribution?

Accepted Answer

It has a mean of 0 and a standard deviation of 1.

Question 11

If a 95% confidence interval for a population mean is (18.6, 24.4), what is the margin of error?

Accepted Answer

$$\frac{24.4 - 18.6}{2} = 2.9$$

Question 12

Which of the following is an example of a discrete random variable?

Accepted Answer

The number of cars passing through an intersection in an hour.

Question 13

A hypothesis test results in a p-value of 0.03. If the significance level is $$\alpha = 0.05$$, what is the correct decision?

Accepted Answer

Reject the null hypothesis.

Question 14

Which of the following is true about mutually exclusive events?

Accepted Answer

They cannot occur at the same time.

Question 15

If the mean of a data set is 50 and the standard deviation is 5, what is the coefficient of variation?

Accepted Answer

$$\frac{5}{50} 	imes 100\% = 10\%$$

Question 16

A survey finds that 25% of households subscribe to a streaming service. If 6 households are selected at random, what is the probability that exactly 2 subscribe? (Let $$p = 0.25$$, $$n = 6$$, $$x = 2)$$

Accepted Answer

$$\binom{6}{2} (0.25)^2$ (0.75)^4$

Question 17

Which of the following best describes the purpose of a confidence interval?

Accepted Answer

To estimate a population parameter with an associated level of confidence.

Question 18

Which of the following is a possible cause of experimental design bias?

Accepted Answer

Confounding variables

Question 19

If a distribution is bell-shaped, what percentage of data falls within two standard deviations of the mean according to the Empirical Rule?

Accepted Answer

About 95%

Comprehensive Study Notes for Introductory Statistics

Guida di studio - Domande di pratica

Study guide - Flashcard