You are conducting a goodness of fit hypothesis test for the claim that all 5 categories are equally likely to be selected (i.e. they do all occur with the same frequency). Give all answers as decimals rounded to 3 places after the decimal point, if necessary. (a) What are the hypotheses of this test? HO PA PB PC PD PE H1: at least one of these proportions is different O Ho: The observed and expected frequencies of the 5 categories are dependent H1: The observed and expected frequencies of the 5 categories are independent Ho: PA - PB - PC PD - PE HI: all of these proportions are different O Ho: The observed and expected frequencies of the 5 categories are independent H1: The observed and expected frequencies of the 5 categories are dependent 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 16 18 D 15 E 16 (c) What is the chi-square test statistic for this data? Test statistic: x-= (d) For a significance level of a = 0.005, what is the chi-square critical value? Critical value: X2= (e) What would be the decision of this hypothesis test? O Reject Ho Fail to reject Ho (f) State the conclusion of this hypothesis test in nontechnical terms. O There is not sufficient evidence to support the claim. 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