You suspect that an unscrupulous employee at a casino has tampered with a die; that is, he is using a loaded die. In order to test this claim, you roll the die 264 times and obtain the following frequencies: Use Table 3.

Category1      2      3      4      5      6        Frequency54      59      32      37      47      35      

Click here for the Excel Data File

a. Choose the appropriate alternative hypothesis to test if the population proportions differ. All population proportions differ from 1/6.Not all population proportions are equal to 1/6.

b-1.Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and your final answer to 2 decimal places.)

Test statistic  

b-2.Approximate the p-value.   0.100 < p-value < 0.2000.050 < p-value < 0.1000.010 < p-value < 0.0250.025 < p-value < 0.0500.005 < p-value < 0.010

c.At the 1% significance level, can you conclude that the die is loaded? Yes since the p-value is less than α.Yes since the p-value is more than α.No since the p-value is less than α.No since the p-value is more than α