Exam 21: Nonparametric Techniques

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. Movie Ratings Teenager Young Adult Middle Age Seni or 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.

The first step in a Wilcoxon rank sum test is to combine the data values in the two samples and assign a rank of 1 to the: A smallest observation. B middle observation. C largest observation. D observation that occurs most frequently.

In a Kruskal-Wallis test, the following statistics were obtained: T₁ = 55, n₁ = 5, T₂ = 54, n₂ = 5, T₃ = 54, n₃ = 5, T₄ = 47, n₄ = 5. What is the most accurate statement that can be made about the p-value of this test?

In a Kruskal-Wallis test for comparing five populations, the test statistic is calculated as H = 10.20. If the test is conducted at the 1% significance level, then: A the null hypothesis will be rejected. B the null hypothesis will not be rejected. C the test results are inconclusive. D the t -test for matched pairs must be used.

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

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. 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?

Compared to parametric tests, non-parametric tests use the information contained in the data: A more effectively. B less effectively. C about the same. D None of these choices are correct.

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. Movie Ratings Teenager Young Adult Middle Age Seni or 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 Using the appropriate statistical table, what statement can be made about the p-value for the 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.

A non-parametric test is one that makes no assumptions about the specific shape of the population from which a sample is drawn.

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 two independent samples, the following statistics are calculated: $n _ { A } = 5$ , $T _ { A } = 22$ , $n _ { B } = 9$ , $T _ { B } = 83$ . a. Which test is used for testing the hypotheses above? b. What is the p-value of this test?

In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly reviewed by university lecturers. Suppose that Cengage Australia publishing company has recently received two manuscripts for statistics books. To help them decide which one to publish, both are sent to 50 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 20 lecturers rate manuscript A as better and 30 rate manuscript B as better. What is the p-value of this test, if we were testing that manuscript B is more highly rated than manuscript A?

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?

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. 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 Can the general manager infer at the 5% significance level that there are differences in the taste ratings of the four dinners?

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. Movie Ratings Teenager Young Adult Middle Age Seni or 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 Do these data provide sufficient evidence to infer at the 5% significance level that there were differences in ratings among the different age categories?

Which of the following is the non-parametric equivalent to the parametric t-test of $\mu _ { D }$ for matched pairs? A. Wil coxon rank sum test B. Kruskal-Wallis test C. Sign test D. Wilcoxon signed rank sum test