PART

1. a) What is the nonparametric alternative to a 1-sample t test for means?

The non-parametric alternative to a 1-sample t test for means is the Wilcoxon signed-rank test

b) What is the nonparametric alternative to a 2-sample t test for means?

The non-parametric alternative to a 2-sample t test for means is the Wilcoxon 2-sample rank-sum test

c) A test to see if three or more means are equal is called ANOVA for analysis of variance. What is the nonparametric alternative to an ANOVA test for means?

The nonparametric alternative to an ANOVA test for means is the Kruskal-Wallis test

2. Explain the advantages and disadvantages of nonparametric tests

Advantages

i. The probability statements that are attained from majority of non-parametric tests are exact and precise probabilities

ii. If the sample sizes being used in the experiment or study are as minimal as 6, there is no other option but to make use of non-parametric tests with the exception that the nature of the population distribution is correctly known.

iii. There are ideal and appropriate tests for the treatment of the observations from samples obtained from numerous dissimilar populations

iv. Tests are accessible for the treatment of data which are intrinsically in ranks in addition to data whose apparently mathematical scores have solely the strong suit of ranks

v. There are methods accessible for treatment of data which are basic classificatory

vi. The non-parametric tests are considerably simpler to study, understand, and apply as compared to parametric tests (Vaughan, 2001).

Disadvantages

i. Non-parametric tests have low power in comparison to parametric tests. This implies that they have low probability in attaining a significant difference is there exists one

ii. Non-parametric tests place a huge dependence on statistical tables (Weiers, 2010).

3. What distribution is used for the Wilcoxon rank sum test?

The distribution that is used for the Wilcoxon rank sum test is the normal distribution

4. What are the conditions for the Kruskal-Wallis test?

The conditions for the Kruskal-Wallis test include the following:

i. The assumption made is that the samples drawn from the population are done in a random manner

ii. There is also the assumption that the observations made from the sample are independent of one another

iii. The measurement scale for the dependent variable ought to be at least ordinal

PART 2

1. A marketing firm tests three different brands of energy drinks to see how many equivalents of potassium per quart each contains. The results are given below.

Brand A Brand B...… 48

= 55.3 48

= 7.3

Therefore the test statistic is 7.3

There are 2 degrees of freedom

2. An engineer wishes to determine if the stopping distance for midsize automobiles is different from that of compact automobiles at 75 mph. The data is shown below.

Automobile 1 2 3 4 5 6 7 8 9 10

Midsize 188 190 195 192 186 194 188 187 214 203

Compact 200 211 206 297 198 204 218 212 196 193

a) State the null and alternate hypotheses.

Null Hypothesis: The stopping distance for midsize automobiles is different from that of compact automobiles at 75 mph

Alternate Hypothesis: The stopping distance for midsize automobiles is not different from that of compact automobiles at 75 mph

b) Use a Wilcoxon rank sum test to determine if there is a difference in…