Probability and Statistics Quizzes - Test Your Knowledge

Question 1

Which of the following is NOT a measure of the center of a data set?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 2

Which of the following is an incorrect application of probability and statistics in engineering?

Accepted Answer

Financial planning

Answer

Reliability analysis

Answer

Statistical process control

Answer

Risk assessment

Question 3

In mechanical engineering, which application of probability and statistics helps evaluate the probability of system or component failure?

Accepted Answer

Reliability analysis

Answer

Design of experiments

Answer

Quality control

Answer

Traffic modeling

Question 4

When flipping two coins at once, what's the likelihood of getting at least one head?

Accepted Answer

3 / 4

Answer

1 / 4

Answer

0

Answer

1 / 8

Question 5

What is the definition of conditional probability?

Accepted Answer

The likelihood of an event happening if another event has already occurred.

Answer

The likelihood of two events occurring independently.

Answer

The likelihood of an event occurring twice in a row.

Answer

The total likelihood of all possible outcomes of an event.

Question 6

In the field of engineering, which of the following is NOT a typical application of probability and statistics?

Accepted Answer

Astrological predictions and horoscopes

Answer

Reliability analysis and assessment

Answer

Quality control and improvement

Answer

Design of experiments and analysis

Question 7

In Bayesian statistics, what is the process called that adjusts a probability distribution based on new information or evidence?

Accepted Answer

Bayesian updating

Answer

Likelihood estimation

Answer

Prioritization

Answer

Posterior inference

Question 8

In Bayesian statistics, which theorem allows us to update our beliefs or hypotheses based on new information?

Accepted Answer

Bayes' theorem

Answer

Neyman-Pearson lemma

Answer

Central Limit Theorem

Answer

Law of Large Numbers

Question 9

In Bayesian statistics, what is the process of adjusting a probability distribution based on new information called?

Accepted Answer

Bayesian updating

Answer

Conjugate prior

Answer

Posterior predictive distribution

Question 10

In a Bernoulli trial, the probability of success is represented by 'p'. What is the probability of failure?

Accepted Answer

1 - p

Answer

0

Answer

p

Answer

p^2

Question 11

When analyzing data and building statistical models, which ethical consideration is crucial?

Accepted Answer

Acknowledging biases and limitations in the data

Answer

Relying exclusively on publicly accessible data sources

Answer

Prioritizing only the statistical significance of findings

Question 12

Which of the following is NOT a method for assessing the goodness-of-fit of a statistical model?

Accepted Answer

C. Correlation analysis

Answer

A. Residual plots

Answer

B. Hypothesis testing

Answer

D. Akaike Information Criterion (AIC) Score

Question 13

Which of the following is a measure of central tendency?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Skewness

Answer

Kurtosis

Question 14

Which of the following is a graphical representation of the probability distribution of a random variable?

Accepted Answer

Histogram

Answer

Box plot

Answer

Line chart

Answer

Scatterplot

Question 15

To compare the means of two independent groups, which statistical test is most appropriate?

Accepted Answer

t-test (two-sample)

Answer

ANOVA (one-way)

Answer

Chi-square test

Answer

Regression analysis

Question 16

Which of the following is NOT an area where probability and statistics find application in the field of engineering?

Accepted Answer

Financial forecasting

Answer

Reliability analysis

Answer

Quality control

Answer

Risk assessment

Question 17

Which of the following is an example of a non-parametric statistical test?

Accepted Answer

Mann-Whitney U test

Answer

t-test

Answer

ANOVA

Answer

Chi-square test

Question 18

Which of the following functions qualifies as a valid cumulative distribution function (CDF) for random variable X?

Accepted Answer

F(x) = 0 for x < 0, F(x) = 1 for x ≥ 0

Answer

F(x) = -1 for x < 0, F(x) = 1 for x ≥ 0

Answer

F(x) = 1 for x < 0, F(x) = 0 for x ≥ 0

Answer

F(x) = x for 0 ≤ x ≤ 1

Question 19

In a two-tailed z-test with a 0.05 significance level, what is the critical value?

Accepted Answer

1.96

Answer

2.33

Answer

2.58

Answer

3.00

Question 20

In hypothesis testing, what is the null hypothesis?

Accepted Answer

There is no significant difference between the groups being compared

Answer

There is a significant difference between the groups being compared

Answer

The sample is representative of the population

Answer

The data is normally distributed

Question 21

What is the purpose of a correlation coefficient?

Accepted Answer

To measure the strength and direction of a linear relationship between two variables

Answer

To determine if there is a significant difference between two groups

Answer

To estimate the mean of a population

Answer

To test a hypothesis about the distribution of a population

Question 22

A random sample of 100 engineers has a mean salary of $85,000 with a standard deviation of $10,000. What is the 95% confidence interval for the population mean salary?

Accepted Answer

($83,000, $87,000)

Answer

($80,000, $90,000)

Answer

($84,000, $86,000)

Answer

($75,000, $95,000)

Question 23

Which of the following is the purpose of hypothesis testing?

Accepted Answer

To make a decision about a population parameter based on sample data

Answer

To estimate a population mean

Answer

To analyze categorical data

Answer

To create a confidence interval

Question 24

A null hypothesis states that there is:

Accepted Answer

No significant difference between groups

Answer

A significant difference between groups

Answer

A correlation between variables

Answer

A statistical relationship between variables

Question 25

Which of the following is NOT a type of statistical inference?

Accepted Answer

Data visualization

Answer

Hypothesis testing

Answer

Confidence interval estimation

Answer

Regression analysis

Question 26

What is the purpose of a confidence interval?

Accepted Answer

To estimate the true population value with a known level of certainty.

Answer

To test whether a hypothesis is true or false.

Answer

To summarize the distribution of a sample.

Answer

To predict future values of a random variable.

Question 27

Which of the following is a limitation of statistical methods?

Accepted Answer

They rely on assumptions that may not always be met.

Answer

They can only be used with large sample sizes.

Answer

They cannot be used to predict the future.

Answer

They are always accurate and reliable.

Question 28

Which of the following is a measure of central tendency?

Accepted Answer

Mean

Answer

Range

Answer

Correlation

Answer

Standard deviation

Question 29

A correlation coefficient of -0.8 indicates a:

Accepted Answer

Strong negative relationship

Answer

Strong positive relationship

Answer

Weak positive relationship

Answer

Weak negative relationship

Question 30

A bag contains 5 red balls and 3 blue balls. If two balls are drawn without replacement, what is the probability of drawing a red ball and then a blue ball?

Accepted Answer

5/12

Answer

2/5

Answer

1/4

Answer

1/5

Question 31

A scatter plot shows a positive correlation between two variables. Which of the following is a possible interpretation?

Accepted Answer

As one variable increases, the other variable tends to increase

Answer

There is no relationship between the two variables

Answer

As one variable increases, the other variable tends to decrease

Question 32

A fair six-sided die is rolled once. What is the probability of rolling an even number?

Accepted Answer

1/2

Answer

1/3

Answer

1/6

Answer

1/4

Question 33

A sample of data has a mean of 50 and a standard deviation of 10. If the data is normally distributed, what percentage of the data is within one standard deviation of the mean?

Accepted Answer

68%

Answer

50%

Answer

95%

Answer

80%

Question 34

A sample of 100 engineering students has an average height of 175 cm with a standard deviation of 5 cm. Construct a 95% confidence interval for the mean height of the population of all engineering students.

Accepted Answer

(173.7, 176.3)

Answer

(172.5, 177.5)

Answer

(170, 180)

Answer

(174.2, 175.8)

Question 35

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Answer

Median

Answer

Mean

Answer

Mode

Question 36

A manufacturing process produces bolts with a diameter that follows a normal distribution with a mean of 10 mm and a standard deviation of 0.2 mm. What is the probability of producing a bolt with a diameter less than 9.8 mm?

Accepted Answer

0.1587

Answer

0.8413

Answer

0.3413

Answer

0.6827

Question 37

A hypothesis test is conducted to determine if a new material is stronger than an existing material. The null hypothesis states that the new material is not stronger. Which of the following is the alternative hypothesis?

Accepted Answer

The new material is stronger

Answer

The new material is weaker

Answer

The null hypothesis cannot be rejected

Answer

The materials have the same strength

Question 38

A fair coin is flipped twice. What is the probability of getting two heads?

Accepted Answer

0.25

Answer

0.125

Answer

0.75

Answer

0.5

Question 39

A sample of 100 students is taken from a population with a population mean of 70 and a population standard deviation of 15. What is the standard error of the mean for this sample?

Accepted Answer

1.5

Answer

0.15

Answer

3

Answer

7

Question 40

A hypothesis test is conducted with a null hypothesis of μ = 100 and an alternative hypothesis of μ ≠ 100. A sample of 50 observations yields a sample mean of 105 with a sample standard deviation of 12. What is the p-value of this test, assuming a two-tailed test and a significance level of 0.05?

Accepted Answer

0.0228

Answer

0.0100

Answer

0.1000

Question 41

A random variable X has the following probability mass function: P(X=0)=0.2, P(X=1)=0.3, P(X=2)=0.4, and P(X=3)=0.1. What is the expected value of X?

Accepted Answer

1.4

Answer

0.2

Answer

1.0

Answer

0.4

Question 42

A chi-squared goodness-of-fit test is conducted to test the hypothesis that the distribution of a categorical variable follows a certain expected distribution. What does the p-value of the test represent?

Accepted Answer

The probability of observing the sample distribution if the null hypothesis is true.

Answer

The probability of rejecting the null hypothesis if it is true.

Answer

The probability of observing the null hypothesis if the sample distribution is true.

Question 43

Which of the following measures summarizes the spread or variability of a dataset?

Accepted Answer

Variance

Answer

Mean

Answer

Mode

Answer

Median

Question 44

The mean of a normal distribution is a measure of its:

Accepted Answer

Central tendency

Answer

Skewness

Answer

Kurtosis

Answer

Probability

Question 45

Which sampling method involves selecting participants from a list or registry that is readily available?

Accepted Answer

Convenience sampling

Answer

Stratified sampling

Answer

Random sampling

Question 46

In a deck of 52 cards, what is the probability of drawing a red or a face card (Jack, Queen, King)? Assume cards are drawn without replacement.

Accepted Answer

11/26

Answer

2/13

Answer

12/52

Answer

1/2

Question 47

Which type of statistical inference allows us to estimate population parameters based on sample data?

Accepted Answer

Statistical estimation

Answer

Descriptive statistics

Answer

Regression analysis

Answer

Hypothesis testing

Question 48

In a one-sample t-test, the alternative hypothesis typically specifies that:

Accepted Answer

The sample mean is different from the hypothesized mean

Answer

The sample mean is equal to the hypothesized mean

Answer

The sample mean is greater than the hypothesized mean

Answer

The sample mean is less than the hypothesized mean

Question 49

In hypothesis testing, what is the probability of rejecting a true null hypothesis?

Accepted Answer

Type I error

Answer

Significance level

Answer

Type II error

Question 50

A hypothesis test is conducted to determine if the mean weight of a population is greater than 100 pounds. The sample mean is 105 pounds, the sample standard deviation is 10 pounds, and the sample size is 50. Using a significance level of 0.05, what is the conclusion of the hypothesis test?

Accepted Answer

Reject the null hypothesis

Answer

Fail to reject the null hypothesis

Answer

Insufficient information is provided to conduct the test.

Answer

The sample mean is not normally distributed.

Question 51

A linear regression model is fitted to a set of data with the following results:

| | | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---| |
| Model: | y = 10 + 2x |
| R-squared: | 0.8 |
| Standard error of the slope: | 1 |

What is the predicted value of y for x = 5?

Accepted Answer

20

Answer

15

Answer

25

Question 52

A correlation coefficient of -0.75 is obtained for a set of data. What does this indicate about the relationship between the variables?

Accepted Answer

Strong negative correlation

Answer

No correlation

Answer

Perfect positive correlation

Answer

Weak positive correlation

Question 53

A chi-square test of independence is conducted with the following data:

| | | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---| |
| | Attribute A | Attribute B |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---| |
| Row 1 | 20 | 30 |
| Row 2 | 40 | 50 |

Calculate the expected value for the cell in Row 1, Column 1.

Accepted Answer

15

Answer

10

Answer

30

Answer

25

Question 54

A non-parametric test is used to compare the medians of two independent samples. Which of the following tests is used for this purpose?

Accepted Answer

Mann-Whitney U test

Answer

Chi-square test

Answer

ANOVA

Answer

t-test

Question 55

In a fair six-sided die, what is the probability of rolling an even number?

Accepted Answer

1/2

Answer

2/3

Answer

1/4

Answer

1/3

Question 56

Given the probability distribution of a discrete random variable X:
P(X = 0) = 0.4
P(X = 1) = 0.3
P(X = 2) = 0.2
P(X = 3) = 0.1
Calculate the expected value of X.

Accepted Answer

1.2

Answer

0.9

Answer

1.8

Question 57

Find the sample mean of the data set {2, 5, 7, 9, 11}.

Accepted Answer

6.8

Answer

5.8

Answer

4.8

Answer

8.8

Question 58

In a normal distribution, what is the area under the curve between z-scores of -1 and 1?

Accepted Answer

0.68

Answer

0.50

Answer

0.75

Answer

0.95

Question 59

A company claims that the average lifespan of their light bulbs is 1000 hours. A sample of 50 light bulbs was tested and the sample mean lifespan was 980 hours with a sample standard deviation of 50 hours. Using a 5% significance level, can this claim be rejected?

Accepted Answer

Yes

Answer

No

Answer

Cannot determine

Answer

Insufficient information

Question 60

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Answer

Mode

Answer

Median

Answer

Mean

Question 61

A regression analysis produces a coefficient of determination of 0.85. What does this indicate?

Accepted Answer

85% of the variation in the dependent variable is explained by the independent variable.

Answer

15% of the variation in the dependent variable is explained by the independent variable.

Answer

The relationship between the variables is strong.

Question 62

The correlation coefficient between two variables X and Y is 0.9. What does this indicate?

Accepted Answer

X and Y are strongly positively correlated.

Answer

X and Y are weakly negatively correlated.

Answer

X and Y are independent.

Answer

X and Y are perfectly correlated.

Question 63

A confidence interval for a population proportion is given as (0.4, 0.6) with a 95% confidence level. What does this mean?

Accepted Answer

We are 95% confident that the true population proportion is between 0.4 and 0.6.

Answer

The sample proportion is 0.5.

Answer

95% of the sample falls within the interval.

Question 64

Which of the following is a key concept in probability theory?

Accepted Answer

Random variable

Answer

Error term

Answer

Causal factor

Answer

Deterministic variable