In Exercise?, ?conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion. Last Digits of Heights? Example 1 in this section involved an analysis of the last digits of weights from a random sample of 100 Californians. Using those same subjects, the last digits of their heights are listed in the table below (based on data from the California Department of Public Health). Use a 0.05 significance level to test the claim that the sample is from a population of heights in which the last digits do ?not? occur with the same frequency. The accompanying Minitab display results from the data in the table. L a s t D i g i t F r e q u e n c y Example 1? Last Digits of Weights

Solution 6BSC L a s t D 0 3 4 5 6 7 8 9 i g i t F r e q 1 1 1 1 u 9 9 8 5 2 1 3 1 e n c y Example 1 Last Digits of Weights Answer: Step 1 By using = 0.05 significance level to test the claim that the sample is from a population of heights in which the last digits do not occur with the same frequency. The Hypotheses here is H : The sample is from a population of heights in which the last digits occur with the same 0 frequency. H1 The sample is from a population of heights in which the last digits do not occur with the same frequency. The accompanying Minitab display results from the data in the table, we have 2 N = 100, degrees of freedom = 9, the Critical Value for = 6.6 with 9 degrees of freedom at 5% level of significance and P-value = 0.679. (The smaller P-value is, the stronger the evidence against H and in favor 0 H . If 1 P-value is small like 0.01 or smaller, we may conclude that the null hypothesis H is 0 strongly rejected in favor of H . If P-value is between 0.05 P-value 0.01, we may 1 conclude that the null hypothesis H is rejec0d in favor of H . In other c1es, i.e., P-value > 0.05, we may conclude that the null hypothesis H is accepted) 0 Since P-value is greater than 0.05 we accept the null hypothesis at 5% level of significance and conclude that there is sufficient evidence to claim that the sample is from a population of heights in which the last digits do not occur with the same frequency.