Appendix B Data Sets.?Refer to the sample data for the given exercise. Use the Wilcoxon signed-ranks test for the claim about the median of a population. Exercise Refer to the indicated data set in Appendix B and use the sign test for the claim about the median of a population. Coke Contents Refer to Data Set 19 in Appendix B for the amounts (in oz) in cans of regular Coke. The cans are labeled to indicate that the contents are 12 oz of Coke. Use a 0.05 significance level to test the claim that cans of Coke are filled so that the median amount is 12 oz. If the median is not 12 oz, are consumers being cheated?
Solution 11BSC Step 1 Given, the amounts (in oz) in cans of regular Coke. The cans are labeled to indicate that the contents are 12 oz of Coke. By using = 0.05 level of significance to test the claim that cans of Coke are filled so that the median amount is 12 oz. The Hypotheses can be expressed as H : Median is equal to 12 oz. 0 H1 Median is not equal to 12 oz. Step 2 Let us denote negative sign (-) for contents less than 12 oz and positive sign (+) for contents more than 12 oz, we have 1 negative signs and 133 positive signs and 2 equal values from the dataset-19 of Appendix B. Now, We have to calculate the positive sum of the ranks. Hence, the positive sum of the ranks is = 133 and We have to calculate the negative sum of the ranks. Therefore the negative sum of the ranks is = -1 Absolute value of sum of the ranks that are negative is 1. Now, The value of the test statistic T is equal to the smaller of the two sums. So the value of the test statistics is 133 Therefore T = 133 Then, here n=27. so here n = 27, which is less than 30. Hence the value of the test statistic is T = 146.5 We know that the level of significance . Now, the Test Statistic is the less frequent sign i.e., negative sign = 1 Therefore, x = 1 is the required value of test statistic. Hence for sign test the required sample size used is 134 i.e., n = 133 + 1 = 134 which is greater than 25 (n 25).