Refer to the indicated data set in Appendix B and use the sign test for the claim about the median of a population. Testing for Median Weight of Quarters? Refer to Data Set 21 in Appendix B for the weights (g) of randomly selected quarters that were minted after 1964. The quarters are supposed to have a median weight of 5.670 g. Use a 0.01 significance level to test the claim that the median is equal to 5.670 g. Do quarters appear to be minted according to specifications?
Solution 17BSC Step 1 Given, the median weight of quarters for the weights (g) of randomly selected quarters that were minted after 1964. By using = 0.01 level of significance to test the claim that the median is equal to 5.670 g. The Hypotheses can be expressed as H : Median is equal to 5.670 0 H1 Median is not equal to 5.670 Step 2 Let us denote negative sign (-) for weights less than 5.670 and positive sign (+) for weights more than 5.670, we have 28 negative signs and 12 positive signs from the dataset-21. Now, Positive signs = 12 Negative signs = 28 Number of ties = 0 Now, the Test Statistic is the less frequent sign i.e., positive sign = 12 Therefore, x = 12 is the required value of test statistic. Hence for sign test the required sample size used is 40 i.e., n = 12 + 28 = 40 which is greater than 25 (n 25).