Question 1

A researcher collects the following data on the number of hours students study per week: 5, 8, 10, 10, 12. What is the mean of this data set?

Accepted Answer

$$\frac{5+8+10+10+12}{5} = 9$$

Question 2

Which of the following best describes the sampling method used when every member of a population has an equal chance of being selected?

Accepted Answer

Random sampling

Question 3

A survey asks respondents to state their favorite color. Is this data quantitative or qualitative?

Accepted Answer

Qualitative

Question 4

Which of the following is an example of discrete data?

Accepted Answer

The number of cars in a parking lot

Question 5

Using the Range Rule of Thumb, estimate the standard deviation for the following data set: 2, 4, 6, 8, 10.

Accepted Answer

$$\frac{10-2}{2} = 4$$

Question 6

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.1$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.3 + 0.5 - 0.1 = 0.7$$

Question 7

In a binomial experiment with $$n = 5$$ trials and $$p = 0.4$$, what is the probability of getting exactly 2 successes?

Accepted Answer

$$\binom{5}{2} (0.4)^2$ (0.6)^3$ = 0.2304$$

Question 8

A hospital reports that the probability of a patient recovering from a certain surgery is 0.85. What is the probability that out of 3 patients, exactly 2 will recover?

Accepted Answer

$$\binom{3}{2} (0.85)^2$ (0.15)^1$ = 0.325$$

Question 9

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.

Question 10

A 95% confidence interval for the mean is calculated as $$\bar{x} \pm 1.96 \frac{s}{\sqrt{n}}. $$What does the value 1.96 represent?

Accepted Answer

The critical value from the standard normal distribution

Question 11

A pharmaceutical company wants to estimate the proportion of patients who experience side effects from a new drug. Which formula should they use to determine the required sample size for a given margin of error $$E$$?

Accepted Answer

$$n = \frac{Z^2$ p (1-p)}{E^2$}$$

Question 12

Which scenario best describes a Type I error?

Accepted Answer

Rejecting a true null hypothesis

Question 13

A researcher performs a hypothesis test and obtains a p-value of 0.03. If the significance level is 0.05, what should the researcher conclude?

Accepted Answer

Reject the null hypothesis

Question 14

Given the following paired data: (2, 3), (4, 5), (6, 7), calculate the linear correlation coefficient $$r.$$

Accepted Answer

$$r = 1$$

Question 15

If the calculated correlation coefficient $$r = 0.85$$ and the critical value $$r_c = 0.70$$, what can you conclude about the linear correlation?

Accepted Answer

There is a significant linear correlation

Question 16

A regression equation is given by $$y = 2x + 1. $$What is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$y = 2 	imes 4 + 1 = 9$$

Question 17

Which of the following is NOT an assumption for performing a hypothesis test for a population mean?

Accepted Answer

The sample mean equals the population mean

Question 18

A student wants to test if the average time spent on homework is different from 2 hours. Which is the correct null hypothesis?

Accepted Answer

$$H_0$$: \mu = 2$$

Question 19

Which formula is used to calculate the margin of error for a population mean when the population standard deviation is known?

Accepted Answer

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

Statistics Final Exam Study Guide: Key Concepts and Applications

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