Question

M17 Problem Set The data in the accompanying table give the weights (ing) of randomly selected quarters that were minted after 1964. The quarters are supposed to have a median weight of 5.670 g. Use the sign test and a 0.01 significance level to test the claim tie the median is less than 5.670 5.647 5.681 5.657 5.696 5.694 5.683 5.656 5.685 5.65 5.643 5.633 5.661 5.652 5.663 5.697 5.681 5.633 5.672 5.687 5.671 5.676 5.666 5.682 5.672 5.666 5.676 5.647 5.649 5.652 5.64 5.623 5.669 5.688 5.661 5.697 5.665 5.652 Find the null and alternative hypothesis. HO: Median weight 5.670 Median weight < 5.670 Median weight 5.670 Median weight > 5.670 Median weight < 5.670 Median weight = 5.670

Answer 1

H₀ : median = 5.670

H₁ : median < 6.57

Step-1:State the hypothesis Ho: population median > 5.67. Hj: population median < 5.67. Step-2: To perform the test, we count number of elements > 5.67 and number of elements < 5.67. We drop elements with value exactly 5.67. In 3rd column, we put + if element is > 5.67,- if element is 5.67 and n/a if element is = 5.67.

# A Sign 1 5.647 2 5.633 3 5.671 + 4 5.652 5 5.681 + 6 5.661 7 5.676 + 8 5.64 9 5.657 10 5.652 11 5.666 12 5.623 13 5.696 + 14 5.663 15 5.682 + 16 5.669 17 5.694 + 18 5.697 + 19 5.672 + + 20 5.688 21 5.683 + + 22 5.681 23 5.666 24 5.661 25 5.656


| 26 5.633 | 27 15.676 十 | 288 5.697 + | 29 5.685 十 30 5.672 十 3115.647 | 32 5.665 | 3315.65 | 3415.687 + | 35 5.649 1 | 365.652 37 5.643 1


Step-3: Number of plus sign = 16 Number of minus sign = 21 n = 16 + 21 = 37 Step-4: p-value = BINOMDIST(16, 37, 0.5, TRUE) = 0.2557 Since the p-value(0.2557) > (0.01) (one-tailed test), we can't reject the null hypothesis Ho

Conclusion about H₀ : we accept it at level 0.01 and fail to reject as theres nt enough evidence against it

Conclusion about the claim : We reject the claim that median < 5.67