Question 1

Which of the following best describes the main purpose of descriptive statistics?

Accepted Answer

To summarize and organize data so it can be easily understood.

Question 2

A researcher collects data on the heights of 100 university students. Which measure would best describe the central tendency of this data if there are no extreme outliers?

Accepted Answer

The mean

Question 3

Suppose you are given the following data set: 2, 4, 4, 6, 8. What is the variance of this data set?

Accepted Answer

$$\frac{1}{4}((2-4.8)^2$ + (4-4.8)^2$ + (4-4.8)^2$ + (6-4.8)^2$ + (8-4.8)^2$) = 5.2$$

Question 4

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 5

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

Accepted Answer

$$\frac{1}{3}$$

Question 6

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

Accepted Answer

It is skewed to the right.

Question 7

A sample of 25 students has a mean test score of 80 and a standard deviation of 10. What is the standard error of the mean?

Accepted Answer

$$\frac{10}{\sqrt{25}} = 2$$

Question 8

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

Accepted Answer

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

Question 9

A pharmaceutical company wants to test if a new drug is more effective than the current standard. Which type of hypothesis test should they use?

Accepted Answer

A one-tailed test

Question 10

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

Accepted Answer

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

Question 11

A researcher is comparing the mean blood pressure of two independent groups. Which statistical test is most appropriate?

Accepted Answer

Independent samples t-test

Question 12

Which of the following is a key assumption of ANOVA (Analysis of Variance)?

Accepted Answer

The variances of the populations are equal.

Question 13

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam scores. What does this indicate?

Accepted Answer

There is a strong positive linear relationship.

Question 14

Which of the following is the correct formula for the regression line?

Accepted Answer

$$y = a + bx$$

Question 15

A hospital wants to compare the proportion of patients who recover within a week using two different treatments. Which statistical test should be used?

Accepted Answer

Test for comparing two proportions

Question 16

Which of the following is NOT a reason to use blocking in experimental design?

Accepted Answer

To increase the number of experimental units.

Question 17

If a 95% confidence interval for the difference in means between two groups is $$(-2, 5)$$, what can you conclude?

Accepted Answer

Zero is included in the interval, so there is no significant difference.

Question 18

Which of the following is a correct interpretation of the coefficient of determination ($$R^2) in $$regression analysis?

Accepted Answer

$$R^2 is $$the proportion of the variance in the dependent variable that is predictable from the independent variable.

Question 19

A researcher wants to test whether a categorical variable (e.g., blood type) is independent of another categorical variable (e.g., disease status). Which test should be used?

Accepted Answer

Chi-square test for independence

Question 20

Which of the following is a potential consequence of violating the assumption of homogeneity of variance in ANOVA?

Accepted Answer

Increased risk of Type I error

TECH-4025 (Applied Statistics) – Course Timeline and Chapter Overview

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