Select a six-sided die and determine if it is fair by conducting a Chi-Square test of goodness of fit. Roll the die 60 times and record the results in the table below along with the predicted number of each of the outcomes.

Roll	Observed Outcome	Expected Outcome
1
2
3
4
5
6

• Calculate the Chi-Squared statistic for this data.

x2 =_____________________________

• Calculate the tail area for this Chi-Squared Test for goodness of fit. Does is accept or reject the null hypothesis at the 10% level of significance?

• Repeat the process for the roll of two dice. Use 72 trials and record the results in the table below. The expected outcomes can be determined using the sample space for the roll of two dice.

Roll	Observed Outcome	Expected Outcome
1
2
3
4
5
6
7
8
9
10
11
12

• Calculate the tail area for this Chi-Squared Test for goodness of fit. Does is accept or reject the null hypothesis at the 10% level of significance?

x2=______________

• Create a set of data using 72 trials that would prove two dice are "loaded", or not consistent with the expected values at the 10% level of significance. Complete the table and calculate the Chi-squared statistic and tail area for this test confirming this.

Roll	Observed Outcome	Expected Outcome
1
2
3
4
5
6
7
8
9
10
11
12

x2= ________________________________________