Exam 21: Nonparametric Techniques

Perform the Wilcoxon signed rank sum test for the following matched pairs to determine at the 10% significance level whether the two population locations differ. Matched Pair 1 2 3 4 5 6 7 A 13 9 11 10 12 8 14 B 11 10 10 6 10 4 12

Which of the following is the alternative hypothesis tested in applications of the Kruskal-Wallis test?

A non-parametric method to compare two populations, when the samples are matched pairs and the data are ordinal, is the:

We can use the Friedman test to determine whether a difference exists between two populations. However, if we want to determine whether one population location is larger than another, we must use the sign test.

Use the 5% significance level to test the hypotheses. $H _ { 0 } :$ The two population locations are the same $H _ { 1 } :$ The two population locations are different, given that the data below are drawn from a matched pair experiment. Matched Pair 1 2 3 4 5 6 7 8 9 10 A 32 15 19 25 39 18 26 41 33 23 B 28 14 20 20 27 23 25 31 25 23

The Friedman test is employed to compare two or more populations when the data are generated from a matched pairs experiment, and are either ordinal or interval but not normally distributed.

In the sign test applications, the normal approximation to the binomial distribution may be used whenever the number of nonzero differences is greater than or equal to:

The sign test is employed to compare two populations when the experimental design is matched pairs, and the data are ordinal but not normally distributed.

In testing the hypotheses: $H _ { 0 } :$ The two population locations are the same $H _ { 1 } :$ The location of population A is to the right of the location of population B, with data drawn from a matched pairs experiment, the following statistics are calculated: $n = 27$ , $T ^ { + } = 271$ , $T ^ { - } = 107$ . a. Which test is used in testing the hypotheses above? b. What is the p-value of this test?

Use the following statistics to determine whether there is enough statistical evidence at the 1% significance level to infer that the population locations differ. T₁ = 90, n₁ = 6, T₂ = 56, n₂ = 6, T₃ = 25, n₃ = 6.

The general manager of a frozen TV dinner maker must decide which one of four new dinners to introduce to the market. He decides to perform an experiment to help make a decision. Each dinner is sampled by ten people who then rate the product on a 7-point scale, where 1 = poor, and 7 = excellent. The results are shown below. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Taste Ratings }$ Respondent Dinner 1 Dinner 2 Dinner 3 Dinner 4 1 6 6 4 5 2 5 5 2 4 3 7 7 3 4 4 6 6 5 4 5 7 6 4 3 6 7 5 3 5 7 6 4 3 4 8 5 6 4 6 9 4 4 3 5 10 7 5 6 4 Using the appropriate statistical table, what statement can be made about the p-value for the test?

The Kruskal-Wallis test uses the Chi-squared distribution.

Which of the following distributions approximates the Kruskal-Wallis test statistic H when the problem objective is to compare k distributions and the sample sizes are greater than or equal to 5?

A movie critic wanted to determine whether or not moviegoers of different age groups evaluated a movie differently. With this objective, he commissioned a survey that asked people their ratings of their most recently watched movies. The rating categories were: 1 = terrible. 2 = fair. 3 = good. 4 = excellent. Each respondent was also asked to categorise his or her age as either: 1 = teenager. 2 = young adult (20-34). 3 = middle age (35-50). 4 = senior (over 50). The results are shown below. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Movie Ratings }$ Teenager Young Adult Middle Age Senior 3 2 3 3 4 3 2 4 3 3 1 4 3 2 2 3 3 2 2 3 4 1 3 4 2 3 1 4 4 2 4 3 Use Excel to find the exact p-value for this test.

Which of the following best describes when the Wilcoxon rank sum test statistic T is approximately normally distributed?

In a Wilcoxon rank sum test, the two sample sizes are 6 and 6, and the value of the Wilcoxon test statistic is T = 20. If the test is two-tailed and the level of significance is $\alpha = 005$ , then:

A supermarket chain has its own house brand of ice cream. The general manager claims that her ice cream is better than the ice cream sold by a well-known ice cream parlour chain. To test the claim, 40 individuals are randomly selected to participate in the following experiment. Each respondent is given the two brands of ice cream to taste (without any identification) and asked to judge which one is better. Suppose that 25 people judge the ice cream parlour brand better, four say that the brands taste the same, and the rest claim that the supermarket brand is better. Which test is appropriate for this situation?

In testing the hypotheses: $H _ { 0 } :$ The two population locations are the same $H _ { 1 } :$ The two population locations are different, with data drawn from a matched pairs experiment, the following statistics are calculated: $n = 40$ , $T ^ { + } = 238$ , $T ^ { - } = 582$ . a. Which test is used for testing the hypotheses above? b. What is the p-value of this test?

Which of the following best describes when to apply the Friedman test to determine whether the locations of two or more populations are the same?

A matched pairs experiment yielded the following results: Number of positive differences = 18, number of negative differences = 7, number of zero differences = 3. Can we infer at the 5% significance level that the location of population 1 is to the right of the location of population 2?