Flipping and Spinning Pennies? Use the data in the table below with a 0.05 significance level to test the claim that when flipping or spinning a penny, the outcome is independent of whether the penny was flipped or spun. (The data are from experimental results given in ?Chance News)?Does the conclusion change if the significance level is changed to 0.01? H e a Tails d s F l i 2 p 0 1992 p 4 i 8 n g S p i 9 n 5 1047 n 3 i n g

Solution 5RE Step1: From the above given problem we have Flipping and Spinning Pennies Heads Tails Flipping 2048 1992 Spinning 953 1047 With = 0.05 level of significance Step2: Our aim is to test the claim that when flipping or spinning a penny, the outcome is independent of whether the penny was flipped or spun. Consider the hypothesis, H 0 When flipping or spinning a penny, the outcome is independent of whether the penny was flipped or spun H : When flipping or spinning a penny, the outcome is not independent of whether the penny 1 was flipped or spun With = 0.05 level of significance Step3: the chi-square test statistic can be calculated by using MINITAB and it is given by Conclusion: 2 From the above output result we have = 4.955 with 1 degrees of freedom and p value is 0.026 comparing this p value with level of significance of , the p value(p = 0.026) is less than level of significance of = 0.05.Hence,we can reject null hypothesis that when flipping or spinning a penny, the outcome is independent of whether the penny was flipped or spun.