Question

You are conducting a Goodness of Fit hypothesis test for the claim that the population data values are not distributed as follows: PA = 0.1; PB = 0.4; Pc = 0.3; pp = 0.2 Give all answers as decimals rounded to 3 places after the decimal point, if necessary. (a) What are the hypotheses for this test? OH:Pa = 0.1, PB = 0.4, pc = 0.3, pp = 0.2 H: all of these proportions are different than what is given in the null hypothesis OH,: The observed and expected frequencies of the 4 categories are independent H : The observed and expected frequencies of the 4 categories are dependent O Ho:Pa = 0.1, p = 0.4, pc = 0.3, pp = 0.2 H1: at least one of these proportions is different than what is given in the null hypothesis O Ho: The observed and expected frequencies of the 4 categories are dependent H1: The observed and expected frequencies of the 4 categories are independent (b) The observed frequencies from a random sample are given in the table below. Find the expected frequencies for this sample, and enter them in the table. Category Observed Expected Frequency Frequency A 10 B. 52

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Answer 1

a) We want to test - HO: PA=0.1, PB :0.4, Pc: 0.3, Po=0.2 Hi: at least one of these propustion different than that given in the null hypothesis b) catagay O; Ei CO; -E;)?/E; A 10 1.094 B 0.233 52 37 139x0.1 2 13.9 139x0.9=55.6 139 x0.3 : 91.7 139 x0.2 : 27.8 С O. 529 D 40 5.353 Total N:139 7.210 () Test Statistica Σ coi - El Ei x²n. I 7.21 d) critical volupa x², 0.025= 9.348 As kecel (9.398 We fail to reject Ho e) Fail to select Ho f) Ans: There is not sufficient evidence to support the claim.