Question

3. This question involves a Test of Independence for the following contingency table. Use a = 0.05. Column 1 Column 3 Column 4 Column 2 50 Row 1 Row 2 75 50 100 50 (a) (2 marks) State the appropriate hypotheses. (b) (8 marks) Create a table of Expected Frequencies. (c) (8 marks) Determine the test statistic. (d) (2 marks) Use the p-value approach. What is your conclusion?

Answer 1

Above problem is solved using Minitab, output of Minitab is attached below

Minitab - Untitled de Cake Graph Editor Tools Window Help Assistant + YENX TOOL aze a CS Colt Cola Cola Cola 50 75 50 100 50 16-04-2020 18:59:13 Welcome to Minitab, press F1 for help. SO 50 Chi-Square Test for Association: Worksheet rows, Worksheet columns Rows: Worksheet rows Columna: Worksheet columns Col 1 Col 2 Col 3 Col 4 ALI 75 62.50 50 75 50.00 87.50 50 250 50.00 50 62.50 50 100 50 250 50.00 87.50 50.00 All 125 100 175 100 500 Cell Contents: Count Expected count Pearson Chi-Square = 8.571, DE - 3, L-Value - 0.036 Likelihood Ratio Chi-Square = 8.618, DE = 3, p-value = 0.035 LHC2222 1922

a) Hypothesis, Ho: Rows and columing are independent. Hii Rows and columns are dependent 6) expected freg 1 Rowl 62.50 1 Rowa 62.30 30 50 87.50 87.50 50 50 c) Test statistics : 8.618 df = 3 d) P-value=0.035 ,2=0.05 P-value (0.035) { x 0.05) Ho is rejected. Rows and columns as dependent of not independent ..

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