Question 1

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize and organize data, while inferential statistics use sample data to make generalizations about a population.

Question 2

A pharmaceutical company wants to compare the effectiveness of two drugs. Which type of sampling method would best ensure that every patient in the population has an equal chance of being selected?

Accepted Answer

Simple random sampling

Question 3

Given the following data set representing the number of defective products found in 10 batches: 2, 3, 5, 2, 4, 3, 5, 2, 4, 3. What is the mode?

Accepted Answer

3

Question 4

Which formula correctly calculates the sample mean $$\bar{x}$$ for a data set with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 5

A hospital records the blood pressure of 100 patients. The data is grouped into intervals. Which type of graph is most appropriate to display this frequency distribution?

Accepted Answer

Histogram

Question 6

If the probability of a patient recovering from a disease is 0.8, what is the probability that two randomly selected patients both recover?

Accepted Answer

$$0.64$$

Question 7

Which of the following is NOT a property of the normal distribution?

Accepted Answer

It has two distinct peaks.

Question 8

A researcher wants to estimate the average height of university students. She selects 50 students at random. Which term best describes the group of 50 students?

Accepted Answer

Sample

Question 9

Which formula is used to calculate the variance $$s^2 of a $$sample with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ and sample mean $$\bar{x}$$?

Accepted Answer

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

Question 10

A factory produces light bulbs. The probability that a bulb is defective is 0.05. If 20 bulbs are tested, what is the expected number of defective bulbs?

Accepted Answer

$$20 	imes 0.05 = 1$$

Question 11

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

Accepted Answer

Rejecting a true null hypothesis

Question 12

A medical study finds a correlation coefficient $$r = 0.85$$ between exercise frequency and cholesterol level. What does this indicate?

Accepted Answer

There is a strong positive linear relationship between exercise frequency and cholesterol level.

Question 13

Which formula is used to calculate the $$z-$$score for a value $$x in a $$population with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 14

A survey asks students to rate their stress level on a scale from 1 to 10. What type of data is collected?

Accepted Answer

Ordinal

Question 15

A researcher wants to test if a new drug is more effective than the current standard. Which hypothesis should be used?

Accepted Answer

Alternative hypothesis: The new drug is more effective than the current standard.

Question 16

A company wants to know if the average salary of its employees is different from the industry average of $$\50$$,000$. Which statistical test is most appropriate?

Accepted Answer

One-sample $$t-$$test

Question 17

If the standard deviation of a data set is zero, what does this indicate about the data?

Accepted Answer

All data values are equal.

Question 18

A biologist records the number of species in different regions. Which measure of central tendency is most affected by extreme values?

Accepted Answer

Mean

Question 19

Which formula is used to calculate the confidence interval for a population mean when the population standard deviation is known?

Accepted Answer

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

Question 20

A study finds that the probability of a randomly selected person being left-handed is 0.1. In a group of 5 people, what is the probability that exactly one person is left-handed? (Assume independence)

Accepted Answer

$$5 	imes 0.1 	imes 0.9^4$

Probability and Statistics Course Syllabus Overview

Guida di studio - Domande di pratica

Study guide - Flashcard