Non-Parametric Statistics for Mechanical Engineering: Quizzes and Practice

Question 1

What is the purpose of distribution-free tests?

Accepted Answer

To make inferences about a population without assuming a specific distribution

Answer

To find the exact distribution of the sample

Answer

To determine the probability of an event occurring

Answer

To test the significance of a difference between two groups

Question 2

Which of the following measures of central tendency is used in the Kruskal-Wallis test?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Standard deviation

Question 3

Which of the following is a characteristic of ordinal data?

Accepted Answer

Can be ranked in order

Answer

Can be added or subtracted

Answer

Has equal intervals between values

Answer

Can be used to calculate ratios

Question 4

What is the purpose of bootstrapping in non-parametric statistics?

Accepted Answer

To estimate the distribution of a statistic without making assumptions about the population distribution

Answer

To test the significance of a difference between two groups

Answer

To find the exact p-value of a test

Answer

To increase the sample size

Question 5

Which of the following is a non-parametric equivalent to the one-way ANOVA?

Accepted Answer

Kruskal-Wallis test

Answer

Friedman test

Answer

Mann-Whitney U test

Answer

Wilcoxon signed-rank test

Question 6

What is the difference between a two-tailed and a one-tailed non-parametric test?

Accepted Answer

Two-tailed tests test for differences in both directions, while one-tailed tests test for differences in only one direction

Answer

Two-tailed tests require larger sample sizes than one-tailed tests

Answer

One-tailed tests are more powerful than two-tailed tests

Answer

There is no difference between two-tailed and one-tailed non-parametric tests

Question 7

Which of the following is NOT a characteristic of non-parametric statistical methods?

Accepted Answer

Based on probability distributions

Answer

Do not require assumptions about data distribution

Answer

Useful for small sample sizes

Answer

Can handle non-normally distributed data

Question 8

Which of these data visualization techniques is commonly used in non-parametric statistics?

Accepted Answer

Box plot

Answer

Histogram

Answer

Bar chart

Answer

Pie chart

Question 9

A mechanical engineer is assessing the durability of two different types of materials. Which non-parametric statistical test would be most suitable for this situation?

Accepted Answer

Mann-Whitney U test

Answer

Chi-square test

Answer

Kruskal-Wallis test

Answer

Spearman's rank correlation coefficient

Question 10

Which of the following measures of central tendency is most applicable to non-parametric data?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Standard deviation

Question 11

What is the primary objective of non-parametric regression analysis?

Accepted Answer

To forecast the value of a dependent variable based on one or more independent variables

Answer

To fit a linear model to the data

Answer

To test for the significance of a relationship between variables

Answer

To determine the distribution of a variable

Question 12

Which of the following is NOT an assumption of the Spearman's rank correlation coefficient?

Accepted Answer

Data must be normally distributed

Answer

Data must be continuous

Answer

Data must be ranked

Answer

The relationship between variables must be linear

Question 13

To select the most appropriate non-parametric test for analyzing data on concrete compressive strength, a researcher should:

Accepted Answer

Examine the data distribution and choose a test suitable for the observed distribution.

Answer

Apply a non-parametric test without considering the data distribution.

Answer

Select the non-parametric test with the simplest methodology.

Answer

Rely on intuition to choose a non-parametric test.

Question 14

In non-parametric statistical methods, which of the following assumptions is typically not made about the data distribution?

Accepted Answer

Normal distribution

Answer

Lack of outliers

Answer

Independence of observations

Answer

Randomness

Question 15

Which of the following non-parametric hypothesis tests is commonly used to compare two independent groups?

Accepted Answer

Mann-Whitney U test

Answer

t-test

Answer

ANOVA

Answer

Chi-square test

Question 16

When analyzing non-parametric data, which data visualization technique is particularly suitable for displaying the distribution of the data?

Accepted Answer

Box plot

Answer

Histogram

Answer

Scatter plot

Answer

Line chart

Question 17

What is a key difference between confidence intervals and prediction intervals?

Accepted Answer

Confidence intervals estimate the population mean, while prediction intervals estimate future observations

Answer

Prediction intervals estimate the population mean, while confidence intervals estimate future observations

Answer

Both confidence and prediction intervals estimate the population mean

Answer

Both confidence and prediction intervals estimate future observations

Question 18

In non-parametric hypothesis testing, the null hypothesis typically assumes that:

Accepted Answer

There is no significant difference between groups

Answer

There is a positive correlation between variables

Answer

The data is normally distributed

Answer

The population mean is known

Question 19

Which of the following is a suitable measure of central tendency for non-parametric data?

Accepted Answer

Median

Answer

Mean

Answer

Standard deviation

Answer

Variance

Question 20

What is the main distinction between a one-tailed and a two-tailed hypothesis test?

Accepted Answer

One-tailed tests assume a specific direction of difference, while two-tailed tests do not

Answer

Two-tailed tests assume a specific direction of difference, while one-tailed tests do not

Answer

One-tailed tests are more powerful than two-tailed tests

Answer

Two-tailed tests are more powerful than one-tailed tests

Question 21

In non-parametric hypothesis testing, the p-value represents:

Accepted Answer

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

Answer

The probability of rejecting the null hypothesis

Answer

The probability of accepting the alternative hypothesis

Answer

The probability of making a Type II error

Question 22

Compared to parametric tests, non-parametric tests generally have:

Accepted Answer

Less statistical power

Answer

Greater statistical power

Answer

Equivalent statistical power

Question 23

Which non-parametric test is appropriate for assessing the difference in medians between two independent groups?

Accepted Answer

Mann-Whitney U test

Answer

Wilcoxon signed-rank test

Answer

Kruskal-Wallis test

Answer

Friedman test

Question 24

What is the primary purpose of a box plot in non-parametric statistics?

Accepted Answer

Visualize data distribution and identify potential outliers

Answer

Calculate mean and standard deviation

Answer

Test hypotheses about the population mean

Answer

Determine correlation between variables

Question 25

In a non-parametric test for the difference between two independent medians, what is the null hypothesis?

Accepted Answer

The two medians are equal

Answer

The two medians are significantly different

Answer

The data follows a normal distribution

Answer

The sample size is adequate for the test

Question 26

When the distribution of data is unknown, what is the advantage of using a non-parametric test over a parametric test?

Accepted Answer

No assumptions are made about the data distribution

Answer

Results are more accurate

Answer

Calculations are simpler

Answer

Interpretation is clearer

Question 27

Which data visualization technique is most appropriate for displaying the distribution of a categorical variable?

Accepted Answer

Bar chart

Answer

Histogram

Answer

Scatter plot

Answer

Box plot

Question 28

A non-parametric test that assesses the association between an ordinal variable and a binary variable is called:

Accepted Answer

Kendall's tau-b

Answer

Mann-Whitney U-test

Answer

Chi-square test

Answer

Wilcoxon rank-sum test

Question 29

When applying non-parametric statistical methods, which of the following should NOT be considered?

Accepted Answer

Assumptions about the distribution

Answer

Sample size

Answer

Data type

Answer

Statistical power

Question 30

What is the graphical representation of the cumulative probabilities of a non-parametric distribution called?

Accepted Answer

Cumulative distribution function

Answer

Probability mass function

Answer

Histogram

Answer

Bar chart

Question 31

Which non-parametric test is used to test the equality of medians between two independent groups?

Accepted Answer

Mann-Whitney U-test

Answer

Chi-square test

Answer

Kruskal-Wallis test

Answer

Friedman test

Question 32

Which of the following accurately describes a key characteristic of non-parametric statistical methods?

Accepted Answer

They are appropriate for data that does not conform to a specific distribution.

Answer

They assume the data follows a normal distribution.

Answer

They are more powerful than parametric methods for all data types.

Answer

They are only applicable to large sample sizes.

Question 33

Which non-parametric test is appropriate for comparing two independent samples?

Accepted Answer

Mann-Whitney U test

Answer

Kruskal-Wallis test

Answer

Friedman test

Answer

Spearman's rank correlation

Question 34

Which graphical representation is commonly used to effectively visualize non-parametric data?

Accepted Answer

Box plot

Answer

Histogram

Answer

Scatter plot

Answer

Pie chart

Question 35

What is the primary purpose of the bootstrapping technique in non-parametric inference?

Accepted Answer

To estimate the sampling distribution of a statistic without assuming a distribution.

Answer

To reduce the bias of a statistical estimator.

Answer

To increase the power of a non-parametric test.

Answer

To determine the significance level of a hypothesis test.

Question 36

Which of the following is a potential limitation of non-parametric statistical methods?

Accepted Answer

They can be less powerful than parametric methods, especially with large sample sizes and normally distributed data.

Answer

They may not provide as much detailed information as parametric methods.

Answer

They are only applicable to small sample sizes.

Answer

They are inherently more difficult to understand than parametric methods.

Question 37

What is the fundamental difference between a one-sided and a two-sided non-parametric hypothesis test?

Accepted Answer

One-sided tests consider only one direction of the alternative hypothesis, while two-sided tests consider both directions.

Answer

One-sided tests are always more powerful than two-sided tests.

Answer

Two-sided tests are always more conservative than one-sided tests.

Answer

One-sided tests are only applicable to small sample sizes.

Question 38

Which of the following is NOT a characteristic of non-parametric statistical methods?

Accepted Answer

Suitable for large sample sizes only

Answer

Do not require assumptions about data distribution

Answer

Robust to outliers and extreme values

Answer

Often used with ordinal or categorical data

Question 39

Which non-parametric test is used to compare the medians of two independent groups?

Accepted Answer

Mann-Whitney U test

Answer

Wilcoxon signed-rank test

Answer

Kruskal-Wallis test

Answer

Chi-square test

Question 40

What is the main purpose of creating a box plot?

Accepted Answer

To visualize the distribution and variability of data

Answer

To calculate the mean and standard deviation

Answer

To perform statistical significance testing

Answer

To test for normality

Question 41

Which assumption must be met for the Kruskal-Wallis test to be valid?

Accepted Answer

Groups are independent and randomly selected

Answer

Data is normally distributed

Answer

Sample size is large enough (n > 30)

Answer

Homogeneity of variance

Question 42

What is the fundamental difference between parametric and non-parametric statistical tests?

Accepted Answer

Parametric tests require assumptions about data distribution, while non-parametric tests do not

Answer

Non-parametric tests are more powerful than parametric tests

Answer

Parametric tests are more robust to violations of assumptions

Answer

There is no difference between parametric and non-parametric tests

Question 43

Which of the following is NOT a type of non-parametric correlation coefficient?

Accepted Answer

Pearson's correlation coefficient

Answer

Spearman's rank correlation coefficient

Answer

Kendall's tau correlation coefficient

Answer

Phi coefficient

Question 44

Why is considering sample size important when using non-parametric statistical tests?

Accepted Answer

Small sample sizes can affect the power of the test

Answer

Large sample sizes can reduce the likelihood of Type II errors

Answer

Sample size does not impact the validity of non-parametric tests

Answer

Non-parametric tests are always valid regardless of sample size

Question 45

The purpose of the Kruskal-Wallis test is to analyze:

Accepted Answer

Difference between three or more medians

Answer

Difference between two medians

Answer

Correlation between two variables

Answer

Normality of a distribution

Question 46

The sign test is employed to test:

Accepted Answer

Difference between two paired samples

Answer

Difference between two independent samples

Answer

Correlation between two variables

Answer

Normality of a distribution

Question 47

Which assumption is NOT required when employing non-parametric methods?

Accepted Answer

Normal distribution of data

Answer

Data independence

Answer

Continuous data

Answer

Ordinal data (at minimum)

Question 48

What is the fundamental distinction between parametric and non-parametric tests?

Accepted Answer

Parametric tests assume data distribution, while non-parametric tests do not

Answer

Non-parametric tests are inherently more powerful than parametric tests

Answer

Parametric tests are more resilient to outliers compared to non-parametric tests

Answer

There is no significant difference between parametric and non-parametric tests

Question 49

The Wilcoxon signed-rank test is used to analyze:

Accepted Answer

Difference between two paired samples

Answer

Difference between two independent samples

Answer

Correlation between two variables

Answer

Normality of a distribution

Question 50

Which of the following is an illustration of a non-parametric measure of central tendency?

Accepted Answer

Median

Answer

Mean

Answer

Standard deviation

Answer

Variance

Question 51

Which of the following is an assumption of parametric statistical methods?

Accepted Answer

The data is normally distributed

Answer

The data is independent

Answer

The variance of the population is known

Answer

The sample size is large

Question 52

Which non-parametric test is used to test the hypothesis that two independent samples have the same median?

Accepted Answer

Mann-Whitney U test

Answer

Kolmogorov-Smirnov test

Answer

Chi-square test

Answer

Kruskal-Wallis test

Question 53

In a box plot, what does the length of the box represent?

Accepted Answer

The interquartile range

Answer

The range of the data

Answer

The standard deviation

Answer

The mean

Question 54

Which of the following is a potential advantage of non-parametric statistical methods?

Accepted Answer

They can be applied to data of any distribution

Answer

They are always more accurate than parametric tests

Answer

They require large sample sizes

Answer

They are only applicable to ordinal data

Question 55

In a Kruskal-Wallis test, what is the null hypothesis?

Accepted Answer

All groups have the same median

Answer

At least one group has a different median

Answer

The medians of all groups are equal to a specified value

Answer

The variance of the groups is equal

Question 56

What is the asymptotic distribution of the Mann-Whitney U statistic?

Accepted Answer

Standard normal distribution

Answer

t-distribution

Answer

Chi-square distribution

Answer

Uniform distribution