Running head: NON PARAMETRIC STATISTICS Non-Parametric Statistics Student’s Name Professor’s Name Course Title Date NON PARAMETRIC STATISTICS 2 A researcher is examining preferences among four new flavors of ice cream. A sample of n = 80 people is obtained. Each person tastes all four flavors and then picks a favorite. The distribution of preferences is as follows. Do these data indicate any significance preferences among the four flavors? Test at the .05 level of significance. Ice Cream Flavor A B C D 12 18 28 22 For this case, the non-parametric chi square test is used at the 0.05 level of significance. Null Hypothesis: H0: There is no statistically significant difference in the people’s preferences among the four flavors. Alternative hypothesis: H1: There is a statistically significant difference in the people’s preferences among the four flavors. Assuming that the null hypothesis was true, the number of people expected to prefer any 𝟖𝟎 given flavor is 20 ( 𝟒 ). The Chi square statistic is obtained by: (𝟏𝟐−𝟐𝟎)∗(𝟏𝟐−𝟐𝟎) 𝟐𝟎 + (𝟏𝟖−𝟐𝟎)∗(𝟏𝟖−𝟐𝟎) 𝟐𝟎 + (𝟐𝟖−𝟐𝟎)∗(𝟐𝟖−𝟐𝟎) 𝟐𝟎 + (𝟐𝟐−𝟐𝟎)∗(𝟐𝟐−𝟐𝟎) 𝟐𝟎 = 6.8 The Critical value is obtained from the Chi-square distribution table as thus: K is the degrees of freedom and it is obtained by the number of groups less one. (K=3, α= 0.05) = 7.814 NON PARAMETRIC STATISTICS ...
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