Question 1

The Wilcoxon rank sum test statistic "T" is approximately normally distributed whenever the sample sizes are larger than:

Accepted Answer

The Wilcoxon rank sum test statistic "T" is approximately normally distributed whenever the sample sizes are larger than 10. The normal approximation is less reliable for smaller sample sizes.

Question 2

Comparing the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B,in order to make 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 groups when the data are not normally distributed, and the sample sizes are small. In this case, the samples are being compared on the basis of the type of fertilizer used, and the test is being used to assess relative effectiveness. The Wilcoxon signed rank test is used for paired data, the sign test is used for single sample data, and the Spearman rank correlation test is used to assess the direction and strength of a relationship between two variables.

Question 3

If for a particular data set,the skewness = -0.2,and the kurtosis equals 2.1,then it can be inferred that:

Accepted Answer

Negative skewness (-0.2) indicates that the data is skewed to the left, while a kurtosis value of 2.1 indicates that the distribution is less spread out than a normal distribution. This combination of characteristics (negative skewness and high kurtosis) is typical of a distribution that is relatively peaked (less variable) and has heavy tails on the left side, as compared to a normal distribution.

Question 4

A goodness-of-fit-test is to be performed to see if consumers prefer any of four package designs (A,B,C,andD)more than the other three.If a random sample of 60 consumers is selected,what is the expected frequency for category A?

Accepted Answer

Since there are four package designs, the expected frequency for each category would be 60/4 = 15. Therefore, the correct answer is C. A and B are not plausible because they are either too small or too large as expected frequencies for a random sample of 60. D could be a possible answer, but it is less likely because it assumes that only one design is preferred by all consumers.

Question 5

The Wilcoxon signed rank test assumes that the population distribution in the difference of paired samples:

Accepted Answer

The Wilcoxon signed rank test assumes that the population distribution in the difference of paired samples is symmetrical. This means that the distribution is similar on both sides of the mean, which is a characteristic of some commonly used distributions, such as the normal distribution.

Question 6

For a chi-square goodness-of-fit-test,the calculated chi-square value is 7.21.If the table chi-square value is 10.645,what is the appropriate decision for this test?

Accepted Answer

In a goodness-of-fit test, we compare the observed (actual) frequencies with the expected frequencies based on a theoretical distribution (null hypothesis). The null hypothesis assumes that there is no significant difference between the observed and expected frequencies. To test this hypothesis, we use the chi-square test statistic, which measures the degree of discrepancy between the observed and expected frequencies.

In this case, the calculated chi-square value is 7.21, which means that there is some discrepancy between the observed and expected frequencies, but it is not large enough to reject the null hypothesis. To make a decision, we compare the calculated chi-square value with the table chi-square value at a given level of significance and degrees of freedom. If the calculated chi-square value is less than the table chi-square value, we fail to reject the null hypothesis; otherwise, we reject the null hypothesis.

Since the table chi-square value is 10.645 and the calculated chi-square value is 7.21, we can see that the calculated value is less than the table value, which means that we fail to reject the null hypothesis. Therefore, the appropriate decision for this test is to fail to reject the null hypothesis.

Question 7

Which of the following is not a reason to prefer a nonparametric test to a parametric test?

Accepted Answer

Nonparametric tests are generally less powerful than parametric tests when the underlying assumptions of normality and homogeneity of variance hold. Therefore, D is not a reason to prefer a nonparametric test. However, A, B, and C are all valid reasons to prefer a nonparametric test over a parametric test.

Question 8

To apply the Wilcoxon rank sum test to determine whether the location of population 1 is different from the location of population 2,the:

Accepted Answer

The Wilcoxon rank sum test is designed to compare two independent samples, meaning that they are not drawn from the same population and are not related in any way. Therefore, option C is the correct choice. Option A is incorrect because samples should be drawn randomly. Option B is incorrect because the Wilcoxon rank sum test does not require matched pairs. Option D is incorrect because the sample size requirement is not applicable for this test.

Question 9

A chi-square goodness-of-fit-test is being used to determine if the observed frequencies and the expected frequencies from six categories are significantly different.If no parameters are estimated from the data,what is the number of degrees of freedom for this test?

Accepted Answer

The number of degrees of freedom for a chi-square goodness-of-fit test is calculated as the number of categories minus one. Since there are six categories, the degrees of freedom would be 6 - 1 = 5.

Question 10

A goodness-of-fit-test is always conducted as a(n):

Accepted Answer

A goodness-of-fit test is typically conducted as an upper-tail test because it assesses whether the observed data significantly deviate from the expected distribution, with large deviations indicating a poor fit.

Question 11

A random sample of n observations,each of which could be classified into exactly one of k categories,is selected.How many degrees of freedom does a goodness-of-fit-test with specified probabilities have?

Accepted Answer

The number of degrees of freedom for a goodness-of-fit-test with specified probabilities is equal to the number of categories (k) minus 1. This is because once we know the frequency counts for k-1 categories, we can determine the frequency count for the last category through subtraction. Therefore, the correct answer is A) k-1.

Question 12

Consider a cell in a contingency table.Given the cell's row total of 200 and a sample size of 1,000,the cell's expected frequency:

Accepted Answer

The expected frequency in a contingency table cell is calculated using the formula (row total * column total) / sample size. Without knowing the column total, it's impossible to determine the expected frequency, hence additional information is needed.

Question 13

Consider a chi-square distributed random variable with 12 degrees of freedom and a significance level of 0.025.The chi-square value from the table is 23.337.Which of the following computed values of the chi-square test statistic would lead us to a decision "fail to reject" the null hypothesis?

Accepted Answer

Since the table value of chi-square is 23.337 at a significance level of 0.025 and with 12 degrees of freedom, any computed chi-square value less than the table value would lead us to fail to reject the null hypothesis. The only computed value less than the table value is 17.12, so the answer is B.

Question 14

If for a particular data set,the skewness = 0.42,and the kurtosis equals 3.85,then we know that:

Accepted Answer

A positive skewness value (0.42) indicates that the data is skewed to the right. A kurtosis value of 3.85 indicates that the distribution has heavy tails and is more spread out than a normal distribution. Therefore, the correct option is B - the data is skewed to the right and the distribution is more spread out than a normal distribution.

Question 15

Suppose that for a random sample of 14 observations of random variables X and Y we compute a Spearman's rank correlation of 0.52.Is there sufficient evidence to reject the null hypothesis of no relationship between X and Y?

Accepted Answer

To determine if there is sufficient evidence to reject the null hypothesis of no relationship between X and Y using Spearman's rank correlation, we need to consider the sample size and the significance level (α). With a sample size of 14 and a Spearman's rank correlation of 0.52, we can reject the null hypothesis at α = 0.10 because the correlation is significant enough at this level, but it may not be strong enough to reject at lower α levels such as 0.05, 0.025, or 0.01 without further statistical tests or critical values.

Question 16

The area to the right of a chi-square value is 0.025.For 5 degrees of freedom,the table value is:

Accepted Answer

For 5 degrees of freedom and an area to the right (upper tail) of 0.025, the chi-square table value is 12.83. This corresponds to a critical value used for hypothesis testing or confidence interval calculations.

Question 17

A chi-square test for independence with 8 degrees of freedom results in a test statistic of 18.21.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that:

Accepted Answer

The answer of A chi-square test for independence with 8...

Question 18

In a chi-square test of a contingency table,the value of the test statistic was χ² = 12.678,and the critical value at α = 0.025 was 14.4494.Thus:

Accepted Answer

The test statistic value of 12.678 is smaller than the critical value of 14.4494 at α = 0.025. Therefore, we fail to reject the null hypothesis at α = 0.025, meaning that there is not enough evidence to suggest a significant association between the variables in the contingency table.

Question 19

A chi-square test for independence with 10 degrees of freedom results in a test statistic of 18.21.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that:

Accepted Answer

Looking at the chi-square table with 10 degrees of freedom, we find that the critical value for a significance level of 0.05 is 18.31. Since our test statistic is 18.21, it falls just below the critical value. Therefore, the p-value must be greater than 0.05 and less than 0.10. Hence, the most accurate statement is C: 0.05 < p-value < 0.10.

Question 20

Consider the following data set: 16,16,17,18,20,21,21,22,23,24,25,27,27,27,27,and 30.The rank assigned to the four observations of value 27 is:

Accepted Answer

The rank assigned to repeated observations is the average of what their ranks would be if they were not tied. For the value 27, the ranks without ties would be 11, 12, 13, and 14. The average of these ranks is (11+12+13+14)/4 = 50/4 = 12.5. However, since ranking starts from 1, and there are 10 values before the first 27, the correct ranks for the 27s should actually be 11, 12, 13, and 14, making the average (11+12+13+14)/4 = 12.5. My initial calculation was correct but my explanation regarding the starting point of ranking was misleading. The ranks indeed are 11, 12, 13, and 14, and the average of these ranks is correctly 12.5, aligning with choice D, not B as initially stated.

Quiz 14: Analysis of Categorical Data

The Wilcoxon rank sum test statistic "T" is approximately normally distributed whenever the sample sizes are larger than:

Comparing the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B,in order to make a general assessment of relative fertilizer effectiveness,may well call for a:

If for a particular data set,the skewness = -0.2,and the kurtosis equals 2.1,then it can be inferred that:

A goodness-of-fit-test is to be performed to see if consumers prefer any of four package designs (A,B,C,andD) more than the other three.If a random sample of 60 consumers is selected,what is the expected frequency for category A?

The Wilcoxon signed rank test assumes that the population distribution in the difference of paired samples:

For a chi-square goodness-of-fit-test,the calculated chi-square value is 7.21.If the table chi-square value is 10.645,what is the appropriate decision for this test?

Which of the following is not a reason to prefer a nonparametric test to a parametric test?

To apply the Wilcoxon rank sum test to determine whether the location of population 1 is different from the location of population 2,the:

A chi-square goodness-of-fit-test is being used to determine if the observed frequencies and the expected frequencies from six categories are significantly different.If no parameters are estimated from the data,what is the number of degrees of freedom for this test?

A goodness-of-fit-test is always conducted as a(n) :

A random sample of n observations,each of which could be classified into exactly one of k categories,is selected.How many degrees of freedom does a goodness-of-fit-test with specified probabilities have?

Consider a cell in a contingency table.Given the cell's row total of 200 and a sample size of 1,000,the cell's expected frequency:

Consider a chi-square distributed random variable with 12 degrees of freedom and a significance level of 0.025.The chi-square value from the table is 23.337.Which of the following computed values of the chi-square test statistic would lead us to a decision "fail to reject" the null hypothesis?

If for a particular data set,the skewness = 0.42,and the kurtosis equals 3.85,then we know that:

Suppose that for a random sample of 14 observations of random variables X and Y we compute a Spearman's rank correlation of 0.52.Is there sufficient evidence to reject the null hypothesis of no relationship between X and Y?

The area to the right of a chi-square value is 0.025.For 5 degrees of freedom,the table value is:

A chi-square test for independence with 8 degrees of freedom results in a test statistic of 18.21.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that:

In a chi-square test of a contingency table,the value of the test statistic was χ² = 12.678,and the critical value at α = 0.025 was 14.4494.Thus:

A chi-square test for independence with 10 degrees of freedom results in a test statistic of 18.21.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that:

Consider the following data set: 16,16,17,18,20,21,21,22,23,24,25,27,27,27,27,and 30.The rank assigned to the four observations of value 27 is:

Quiz 14: Analysis of Categorical Data

The Wilcoxon rank sum test statistic "T" is approximately normally distributed whenever the sample sizes are larger than:

Comparing the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B,in order to make a general assessment of relative fertilizer effectiveness,may well call for a:

If for a particular data set,the skewness = -0.2,and the kurtosis equals 2.1,then it can be inferred that:

A goodness-of-fit-test is to be performed to see if consumers prefer any of four package designs (A,B,C,andD) more than the other three.If a random sample of 60 consumers is selected,what is the expected frequency for category A?

The Wilcoxon signed rank test assumes that the population distribution in the difference of paired samples:

For a chi-square goodness-of-fit-test,the calculated chi-square value is 7.21.If the table chi-square value is 10.645,what is the appropriate decision for this test?

Which of the following is not a reason to prefer a nonparametric test to a parametric test?

To apply the Wilcoxon rank sum test to determine whether the location of population 1 is different from the location of population 2,the:

A chi-square goodness-of-fit-test is being used to determine if the observed frequencies and the expected frequencies from six categories are significantly different.If no parameters are estimated from the data,what is the number of degrees of freedom for this test?

A goodness-of-fit-test is always conducted as a(n) :

A random sample of n observations,each of which could be classified into exactly one of k categories,is selected.How many degrees of freedom does a goodness-of-fit-test with specified probabilities have?

Consider a cell in a contingency table.Given the cell's row total of 200 and a sample size of 1,000,the cell's expected frequency:

Consider a chi-square distributed random variable with 12 degrees of freedom and a significance level of 0.025.The chi-square value from the table is 23.337.Which of the following computed values of the chi-square test statistic would lead us to a decision "fail to reject" the null hypothesis?

If for a particular data set,the skewness = 0.42,and the kurtosis equals 3.85,then we know that:

Suppose that for a random sample of 14 observations of random variables X and Y we compute a Spearman's rank correlation of 0.52.Is there sufficient evidence to reject the null hypothesis of no relationship between X and Y?

The area to the right of a chi-square value is 0.025.For 5 degrees of freedom,the table value is:

A chi-square test for independence with 8 degrees of freedom results in a test statistic of 18.21.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that:

In a chi-square test of a contingency table,the value of the test statistic was χ2 = 12.678,and the critical value at α = 0.025 was 14.4494.Thus:

A chi-square test for independence with 10 degrees of freedom results in a test statistic of 18.21.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that:

Consider the following data set: 16,16,17,18,20,21,21,22,23,24,25,27,27,27,27,and 30.The rank assigned to the four observations of value 27 is:

In a chi-square test of a contingency table,the value of the test statistic was χ² = 12.678,and the critical value at α = 0.025 was 14.4494.Thus: