2 1. Kelly throws a tetrahedral die n times and records the number on which it lands for each throw. She calculates the expected frequency for each number to be 43 if the die was unbiased. The table below shows three of the frequencies Kelly records but the fourth one is missing. Number 1 2 3 4 Frequency 47 34 36 x (a) Show that x = 55 (1) Kelly wishes to test, at the 5% level of significance, whether or not there is evidence that the tetrahedral die is unbiased. (b) Explain why there are 3 degrees of freedom for this test. (1) (c) Stating your hypotheses clearly and the critical value used, carry out the test. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________