You are conducting a Goodness of Fit hypothesis test for the claim that the population data values are not distributed as follows: PA = 0.3; PB = 0.3; pc = 0.2; PD = 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? Ho: PA = 0.3, PB = 0.3, PC = 0.2, PD = 0.2 Hi: all of these proportions are different than what is given in the null hypothesis O Ho: PA = 0.3, PB = 0.3, PC = 0.2, PD - 0.2 Hi: 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 independent H1: The observed and expected frequencies of the 4 categories are dependent 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 48 53 19 48 (c) What is the chi-square test-statistic for this data? Test Statistic: x = (d) For a significance of level alpha = 0.025, what is the chi-square critical value? Critical Value: X-= (e) What would be the decision of this hypothesis test? O Fail to reject Ho O Reject Ho (f) State the conclusion in nontechnical terms. O There is sufficient evidence to warrant rejection of the claim. O There is not sufficient evidence to warrant rejection of the claim. O There is sufficient evidence to support the claim. O There is not sufficient evidence to support the claim