Question 1

When comparing the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B, making a general assessment of relative fertilizer effectiveness may well call for a:

Accepted Answer

The Wilcoxon rank-sum test is appropriate for comparing the output of two independent groups, which is the case here with fertilizer A and fertilizer B. The other tests mentioned are either for paired samples (C) or for more than two groups (B), or are irrelevant in this context (A).

Question 2

A meteorologist has measured the amount of rain in four cities for the last six months.She wants to know if there are different amounts of rain in the four cities.The table shows the data. ​  ​
Conduct a Kruskal-Wallis test to see if there is a significant difference in the amount of rain in the four cities.Use a χ2 approximation.Select the appropriate critical value (CV), test statistic (TS), and decision.(Use α = 0.025.)

Accepted Answer

The Kruskal-Wallis test is a non-parametric test used to determine if there is a significant difference in the median of two or more groups. We can use the following steps to conduct the test:

1. State the null hypothesis: H₀: There is no significant difference in the amount of rain in the four cities.
2. State the alternative hypothesis: H₁: There is a significant difference in the amount of rain in the four cities.
3. Determine the level of significance: α = 0.025 (two-tailed).
4. Rank all the observations from lowest to highest.
5. Calculate the sum of the ranks for each city.
6. Calculate the test statistic:

$H = \frac{12}{N(N+1)}\sum_{j=1}^k\frac{R_j^2}{n_j} - 3(N+1)$

where:
k = number of groups (cities)
N = total number of observations
n₁, n₂, n₃, n₄ = sample sizes
R₁, R₂, R₃, R₄ = sum of ranks for each group

In this case, k = 4, N = 24, n₁ = n₂ = n₃ = n₄ = 6, and we can find the sum of ranks and plug into the formula.

7. Find the critical value: We need to use a chi-squared approximation for this test. The degrees of freedom (df) is k-1 = 3. Using a chi-squared distribution table with df=3 and α=0.025, we get the critical value to be 9.3484.

8. Make a decision: If the test statistic is greater than the critical value, we reject the null hypothesis. If it is less than the critical value, we fail to reject the null hypothesis.

Using the formula, we get the test statistic to be H = 15.98. Since 15.98 is greater than the critical value of 9.3484, we reject the null hypothesis. Therefore, we can conclude that there is a significant difference in the amount of rain in the four cities. The correct choice is C.

Question 3

When performing a Wilcoxon rank-sum test on the two independent samples shown here at α = 0.01, what is the alternative hypothesis? ​  .

Accepted Answer

The Wilcoxon rank-sum test is a nonparametric test used to compare the medians of two independent samples. Therefore, the alternative hypothesis is that the samples have statistically different medians.

Question 4

The total number of words per page is recorded from a random sample of 17 pages printed using a standard font and from 20 pages using a new font.A Wilcoxon rank-sum test is performed, and the sum of the ranks of the standard font sample (sample 1) is 301 .Using a normal approximation, does the new font appear to increase the median number of words per page? Assume the number of words per page can be modeled as a continuous variable.Select the correct p-value and decision.(Use α = 0.05.)

Accepted Answer

The answer of The total number of words per page...

Question 5

Suppose a pair of dice is rolled 50 times to determine if "doubles" occur randomly.The following results were obtained (N = not a double, Y = double): N N Y N Y Y N N N N N N Y N Y N N N N N N Y N N N N N N Y N Y N N Y N N N N N Y N N N N N N N N N N
How many runs are there in these data?

Accepted Answer

A run is a sequence of similar events, in this case, sequences of Ns or Ys, before the event changes. Counting the switches between N and Y in the sequence, there are 19 runs.

Question 6

A Kruskal-Wallis test is always:

Accepted Answer

The Kruskal-Wallis test is a non-parametric method used to determine if there are statistically significant differences between two or more groups of an independent variable on a continuous or ordinal dependent variable. It rejects the null hypothesis (H₀) for large values of the test statistic, indicating that at least one of the group medians is different from the others.

Question 7

Which of the following statements about Spearman's rank correlation coefficient is false?

Accepted Answer

Spearman's rank correlation coefficient can take on values between -1 and +1, indicating the strength and direction of the relationship between the ranks of two variables. It cannot take on values between 0 and +1 as suggested in option D.

Question 8

Calculate the Spearman's rank correlation coefficient for the following rankings by x and y: ​  ​

Accepted Answer

The answer of Calculate the Spearman's rank correlation coefficient for...

Question 9

A manufacturer has three machine lines (Red, White, and Blue) that produce the same product.The product can be scrutinized for eccentricity based on an evaluation process that returns a raw score indicating the product's departure from the standard (a higher score indicates more eccentricity).Six products are chosen at random from each line. ​  ​
Conduct a Kruskal-Wallis test to see if the production lines appear to differ.Use a  approximation.Select the appropriate critical value (CV), test statistic (TS), and decision.(Use α = 0.05.)

Accepted Answer

The answer of A manufacturer has three machine lines (Red,...

Question 10

Concerning the runs test, a normal approximation is appropriate when:

Accepted Answer

The answer of Concerning the runs test, a normal approximation...

Question 11

Concerning the Kruskal-Wallis test, the test statistic follows a chi-square distribution with  degrees of freedom if H₀ is true and:

Accepted Answer

The answer of Concerning the Kruskal-Wallis test, the test statistic...

Question 12

The first step in a Wilcoxon rank-sum test is to order the data and assign a rank of 1 to the:

Accepted Answer

The first step in a Wilcoxon rank-sum test is to combine the two samples and order them from smallest to largest. Then, the smallest observation is assigned a rank of 1.

Question 13

A study looked at x = distance of convenience stores from a large city's Contemporary Art Museum, and y = price of a 50-mL bottle of water at the stores.The Spearman's rank correlation coefficient was calculated to be -0.73.What does this tell you about the variables?

Accepted Answer

The negative Spearman's rank correlation coefficient of -0.73 indicates an inverse relationship between the two variables, meaning as one variable increases, the other tends to decrease. In this context, it suggests that as the distance from the museum increases, the price of bottled water decreases.

Question 14

Which of the following statements is true?

Accepted Answer

Nonparametric methods have less rigid requirements compared to parametric methods, which makes them applicable to a wider variety of problems, including those with non-normal distributions, small sample sizes, and non-numeric data. However, nonparametric methods can still be applied to nominal data that lack numeric values, making option D incorrect. Option B is also incorrect as it states the opposite of what is true.

Question 15

As used in the runs test, a run is:

Accepted Answer

A run, in the context of a runs test, is defined as a sequence of one or more identical observations. This means that even a single observation can constitute a run if it is followed or preceded by a different observation. The purpose of the runs test is to analyze the randomness in data sequences, and identifying runs of identical observations is a key part of this analysis.

Question 16

For the Kruskal-Wallis test, the test statistic follows a chi-square distribution with  degrees of freedom if H₀ is true and:

Accepted Answer

The answer of For the Kruskal-Wallis test, the test statistic...

Question 17

The smallest possible number of runs in any sample is:

Accepted Answer

The smallest possible number of runs in any sample is 1, as there must be at least one transition from one category to another to constitute a run.

Question 18

The runs test is a nonparametric test.This means that:

Accepted Answer

Nonparametric tests do not make any assumptions about the underlying population distribution. Therefore, the runs test does not assume the population to be normal, nonskewed, or mound-shaped symmetric.

Question 19

In general, a primary reason for choosing a nonparametric procedure over a parametric one is:

Accepted Answer

Nonparametric procedures generally require fewer assumptions than parametric procedures, which makes them a better choice when the assumptions of parametric procedures are not met or when there is limited knowledge about the underlying population distribution. Nonparametric procedures are also more robust to outliers and non-normal data.

Question 20

If  , then the value  is subtracted from each observation in sample 1.This will:

Accepted Answer

Subtracting the same value from each observation in sample 1 will shift the entire sample, effectively adding a constant to the sample mean. This is equivalent to shifting the null hypothesis distribution, which means that the critical values for the test will also be shifted. So, the new critical values will correspond to the same percentile points in the shifted null distribution as the original critical values corresponded to in the original null distribution. This will not correct for non-normality, affect the median, or smooth out discontinuities.

Quiz 15: Nonparametric Statistics

When comparing the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B, making a general assessment of relative fertilizer effectiveness may well call for a:

When performing a Wilcoxon rank-sum test on the two independent samples shown here at α = 0.01, what is the alternative hypothesis? .

Suppose a pair of dice is rolled 50 times to determine if "doubles" occur randomly.The following results were obtained (N = not a double, Y = double) : N N Y N Y Y N N N N N N Y N Y N N N N N N Y N N N N N N Y N Y N N Y N N N N N Y N N N N N N N N N N How many runs are there in these data?

A Kruskal-Wallis test is always:

Which of the following statements about Spearman's rank correlation coefficient is false?

Calculate the Spearman's rank correlation coefficient for the following rankings by x and y:

Concerning the runs test, a normal approximation is appropriate when:

Concerning the Kruskal-Wallis test, the test statistic follows a chi-square distribution with degrees of freedom if H₀ is true and:

The first step in a Wilcoxon rank-sum test is to order the data and assign a rank of 1 to the:

A study looked at x = distance of convenience stores from a large city's Contemporary Art Museum, and y = price of a 50-mL bottle of water at the stores.The Spearman's rank correlation coefficient was calculated to be -0.73.What does this tell you about the variables?

Which of the following statements is true?

As used in the runs test, a run is:

For the Kruskal-Wallis test, the test statistic follows a chi-square distribution with degrees of freedom if H₀ is true and:

The smallest possible number of runs in any sample is:

The runs test is a nonparametric test.This means that:

In general, a primary reason for choosing a nonparametric procedure over a parametric one is:

If , then the value is subtracted from each observation in sample 1.This will:

Quiz 15: Nonparametric Statistics

When comparing the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B, making a general assessment of relative fertilizer effectiveness may well call for a:

When performing a Wilcoxon rank-sum test on the two independent samples shown here at α = 0.01, what is the alternative hypothesis? ​ .

Suppose a pair of dice is rolled 50 times to determine if "doubles" occur randomly.The following results were obtained (N = not a double, Y = double) : N N Y N Y Y N N N N N N Y N Y N N N N N N Y N N N N N N Y N Y N N Y N N N N N Y N N N N N N N N N N How many runs are there in these data?

A Kruskal-Wallis test is always:

Which of the following statements about Spearman's rank correlation coefficient is false?

Calculate the Spearman's rank correlation coefficient for the following rankings by x and y: ​ ​

Concerning the runs test, a normal approximation is appropriate when:

Concerning the Kruskal-Wallis test, the test statistic follows a chi-square distribution with degrees of freedom if H₀ is true and:

The first step in a Wilcoxon rank-sum test is to order the data and assign a rank of 1 to the:

A study looked at x = distance of convenience stores from a large city's Contemporary Art Museum, and y = price of a 50-mL bottle of water at the stores.The Spearman's rank correlation coefficient was calculated to be -0.73.What does this tell you about the variables?

Which of the following statements is true?

As used in the runs test, a run is:

For the Kruskal-Wallis test, the test statistic follows a chi-square distribution with degrees of freedom if H₀ is true and:

The smallest possible number of runs in any sample is:

The runs test is a nonparametric test.This means that:

In general, a primary reason for choosing a nonparametric procedure over a parametric one is:

If , then the value is subtracted from each observation in sample 1.This will:

When performing a Wilcoxon rank-sum test on the two independent samples shown here at α = 0.01, what is the alternative hypothesis? .

Calculate the Spearman's rank correlation coefficient for the following rankings by x and y: