You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies: Ho : PA = 0.4; PB = 0.1; pc = 0.3; PD = 0.2 Complete the table. Report all answers accurate to three decimal places. Observed Expected Category Frequency Frequency A 23 19.75 X B 10 19.75 X C 20 D 26 What is the chi-square test-statistic for this data? (2 decimal places) x = What is the P-Value? (3 decimal places) P-Value = For significance level alpha 0.005, What would be the conclusion of this hypothesis test? O Fail to reject the Null Hypothesis O Reject the Null HypothesisEyeglassomatic manufactures eyeglasses for different retailers. They test to see boy.r many defective lenses they made the time period of January '1 to March 31. The table gives the defect and the number of defects. Do the data support the notion that each defect type occurs in the same proportion? Test at the 1096 level. Number of Defective Lenses Defect type Number of defects State the hypotheses. Hg: Each defect type 0\" in the same proportion. Ha: Each defect type V o" in the same proportion. Calculate the x1 test statistic. Round expected values to two decimal places. Round x3 to three decimal places. x2 = Calculate the p-yalue. Round to four decimal places. p-yalue = State your decision. Since pvalue-'r' o\" [1104 o\" H0. Interpret the results. At the 1693 signficance LeveL there _" o" enough evidence to conclude that each defect type _' o\" in the same proportion. You are conducting a multinomial GoodnessofFit hypothesis test for the claim that not all 5 categories are equally likely to be selected at the significant level of or = Ill. 1. For this study, we should use Ch'-Souaro Test for Goodness of Fit vIV' o" 2. Your friend Nina helped you with the null and alternative hypotheses... 1 Ho:P1=P2=Ps=?4=Ps:E H 1 : At Least one of the categories has a different probability of being selected. You drewr ?3 samples, and the observed frequencies are recorded below. Please complete the table using exact answers {e.g., whole numbers or decimal]. . Observed Expected Categories Frequency Frequency 3. The degree of freedom = The test-statistic for this data = {Please show your answer to three decimal places.) 5. The p-value is lossthan [or equal to: v " or oii a. Base on this. we should '-' hypothesis oi\" 1.11s such. the final conclusion is that... ' Base on the sample data, there is not sufficient evidence to conclude the claim that not all 5 categories are equally likely to be selected at the significant level of or = 0.1. O Base on the sample data, there is sufficient evidence to conclude the claim that not all 5 categories are equally likely to be selected at the significant level of or = 0.1. Researchers watched groups of dolphins to determine what activities the dolphins partake in at certain times of the day. The numbers in the table represent the number of groups of dolphins that were partaking in an activity at certain times of days. Is there enough evidence to show that the activity and the time period are dependent for dolphins? Test at the 5% level. Dolphin Activity Activity Evening Total State the hypotheses. Hg: Activity and the time period are V' o" . Ha: Activity and the time period are - oi" . Calculate the test statistic. Round your answer to three decimal places. x3 = 15.3922 Calculate the p-value. Round your answer to four decimal places. p-value = 0.0143 x State you r decision. Since pvalue-V' o" BLISSV' o" Hg. Interpret your decision in the context of the problem. At the 596 level of significance, there " o' enough evidence to show that activity and the time period are " o\" . Given the 5 categories in the table below, test the claim that the categories are equally likely to be selected at a or = [L significance level. Cote 0 Observed Expected 3. W Frequencyr Frecluencjrlr C '15 4 '14 'l? '13 a. Complete the table by calculating the expected frequencies. b. What is the chi-square test statistic? Round to three decimal places. X2: c. What are the degrees of freedom? d. f.= d. What is the p-value for this sample? Round to four decimal places. p-value = e. Is the p-value less than a? -" o\" f. Make a decision. Failto rojocttaonull. V 'I 0" g. Make a conclusion. There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected. There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected. The sample data support the claim that all 5 categories are equally likely to be selected. There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected. A machine drops balls randomly into 5 bins labeled A, B, C, D, and E. If the machine is working correctly, all bins should end up with the same number of balls. Is there eyidence that the machine is not working correctly? Bin Label OMEN\" EXPECtEd Frequency HFrequencyl Report all answers accurate to three decimal places. But retain unrouna'eo' numbers Jfor future calculations. What is the chisquare teststatistic for this data? {Report answer accurate to three decimal places. and remember to use the unrounded Pearson residuals in your calculations} 22 = What are the degrees of freedom for this test? d.f.= is What is the p-value for this sample? {Report answer accurate to four decimal places.} The p-value is... less than [or equal to} o; a greater than or This test statistic leads to a decision to... reject the null accept the null fail to reject the null accept the alternative As such. the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that all 5 bins are equally likely to be selected. There is not sufficient evidence to warrant rejection of the claim that all 5 bins are equally likely to be selected. The sample data support the claim that all 5 bins are equally likely to be selected. There is not sufficient sample evidence to support the claim that all 5 bins are equally likely to be selected. You are conducting a test of independence for the claim that two different categories are independent. Here is the sample data. Category C D A 24 60 B 51 19 The expected observations for this table would be Category C D A B 0 - EY The resulting are: E Category C D A B What is the chi-square test-statistic for this data? 29.91What is the P-Value for this test-statistic? What conclusion can you make about the hypothesis? OYes, the proportions of each characteristic are the same in each population. No, the proportions of each characteristic are not the same in each population. 05'!" Report all answers accurate to three decimal places. Report all answers accurate to three decimal places