Question 1

Under the null hypothesis that the population distribution is normal,the test statistic for the Jarque-Bera test for normality has a chi-square distribution with 2 degrees of freedom.

Accepted Answer

This is correct as the Jarque-Bera test for normality is based on the assumption that the population distribution is normal and the test statistic is approximately chi-square distributed with 2 degrees of freedom under the null hypothesis.

Question 2

The Spearman rank correlation coefficient r_s can be seriously affected by extreme observations.

Accepted Answer

The Spearman rank correlation coefficient is based on the ranks of the data rather than their numerical values, making it less sensitive to extreme observations compared to other correlation measures like Pearson's.

Question 3

Kurtosis is a statistic of a data set that describes the symmetry of the data.

Accepted Answer

Kurtosis is a statistic that describes the peakedness (or flatness) of a distribution, not its symmetry.

Question 4

The normal approximation to the sign test is acceptable if the sample size exceeds 15.

Accepted Answer

The answer of The normal approximation to the sign test...

Question 5

The procedure for the Wilcoxon rank sum test requires that we rank each group separately rather than combining them together before assigning ranks.

Accepted Answer

In the Wilcoxon rank sum test, the data from both groups are combined into a single set before the ranks are assigned, not ranked separately within each group.

Question 6

A measure of correlation that is not susceptible to serious influence by extreme values and on which valid tests can be based on general population distributions is obtained through the use of ranks.

Accepted Answer

This statement is true. The use of ranks in correlation analysis reduces the influence of extreme values and permits the use of valid tests on general population distributions.

Question 7

The distribution of the Mann-Whitney statistic,U,approaches the normal distribution quite rapidly as the number of sample observations increases.The approximation is adequate if n₁ ≥ 10 and n₂ ≥ 10.

Accepted Answer

This statement is true. As the sample size increases, the Mann-Whitney U statistic approaches a normal distribution, and the approximation is acceptable if the sample sizes are large enough (usually defined as n1U/B ≥ 10 and n2U/B ≥ 10).

Question 8

If the measure of kurtosis for a particular data set is equal to 1.2,then the distribution of the data appears to be more concentrated than a normally distributed variable with the same mean and variance.

Accepted Answer

A kurtosis value of 1.2 indicates that the distribution is more peaked and has heavier tails than a normal distribution. Therefore, the data is more concentrated around the mean than a normally distributed variable with the same mean and variance.

Question 9

Minitab statistical software can be used to determine confidence intervals for the median based on the sign test.

Accepted Answer

Minitab can be used to determine confidence intervals for the median based on the sign test.

Question 10

Whenever the expected frequency of a cell is less than 5,one remedy for this condition is to decrease the significance level.

Accepted Answer

Decreasing the significance level is not a recommended remedy for when the expected frequency of a cell is less than 5. Instead, one can combine neighboring cells or use exact tests like Fisher's exact test or the chi-squared test with simulated p-values.

Question 11

One disadvantage of nonparametric tests is that,under the assumption of normality in the population,nonparametric procedures are less powerful.

Accepted Answer

Nonparametric tests are designed to be used when assumptions of normality or equal variances are not met. However, when the assumptions of normality are met, parametric tests are usually more powerful than nonparametric tests. Therefore, one disadvantage of nonparametric tests is lower power in comparison to parametric tests when normality assumptions are met.

Question 12

One disadvantage of the sign test is that it takes into account only a very limited amount of information - namely,the signs of the differences.

Accepted Answer

The sign test only considers the signs of the differences between pairs of observations and disregards the magnitude of these differences. Therefore, it uses a limited amount of information and may not provide a comprehensive picture of the data.

Question 13

If the parameters of the distribution of interest are not specified,it is impossible to perform a goodness-of-fit test.

Accepted Answer

Goodness-of-fit tests can still be performed using non-parametric methods or by estimating the parameters from the sample data itself before conducting the test.

Question 14

In order for the chi-square test of independence to be valid,the expected frequency in each cell of the contingency table should be at least 1.

Accepted Answer

The rule of thumb for the chi-square test of independence is that the expected frequency in each cell of the contingency table should be at least 5, not 1, to ensure the validity of the test.

Question 15

If the measure of skewness for a particular data set is positive then the data is skewed to the right.

Accepted Answer

This statement is true as a positive skewness value indicates that the tail of the distribution is longer on the right side, which means that the data is skewed to the right.

Question 16

The method for determining the number of degrees of freedom for the chi-square distribution depends on the type of test being done.

Accepted Answer

The number of degrees of freedom for the chi-square distribution depends on the type of test being done, such as goodness of fit or independence test.

Question 17

The value of the X² statistics can range from -∞ to + ∞.

Accepted Answer

The X² statistic, as described, does not correspond to any known statistical measure or notation in standard statistical analysis or theory.

Question 18

The chi-square distribution approaches the normal distribution as the degrees of freedom becomes larger.

Accepted Answer

As the degrees of freedom increases, the shape of the chi-square distribution becomes more symmetric and bell-shaped, similar to the normal distribution. Therefore, the chi-square distribution approaches the normal distribution as the degrees of freedom increase.

Question 19

The Wilcoxon rank sum test is similar to the Mann-Whitney U test.The results will be the same for both tests.

Accepted Answer

The Wilcoxon rank sum test and the Mann-Whitney U test are two names for the same test, so the results will always be the same.

Question 20

The Wilcoxon rank sum test provides a method to incorporate information about the magnitude of the differences between matched pairs.

Accepted Answer

The Wilcoxon rank sum test is used for independent samples and does not involve matched pairs. The Wilcoxon signed-rank test is the one that deals with matched pairs and accounts for the magnitude of the differences.

Quiz 14: Analysis of Categorical Data