Exam 21: Nonparametric Techniques

In a normal approximation to the Wilcoxon rank sum test, the standardised test statistic is calculated as z = 1.80. For a two- tail test, the p-value is:

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

Which of the following best describes when a non-parametric test for comparing two or more populations should be used instead of its parametric counterpart?

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. Use Excel to find the exact p-value for this test.

A non-parametric method to compare two populations, when the samples are independent but the assumptions behind the independent samples t-test are violated, is the:

If in a matched pairs experiment we find 20 negative, 8 zero, and 10 positive differences, perform the sign test at the 10% significance level to determine whether the two population locations differ.