Dice After getting trounced by your little brother in a childrens game, you suspect the die he gave you to roll may be unfair. To check, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the dies fairness? a) If the die is fair, how many times would you expect each face to show? b) To see if these results are unusual, will you test goodness-of-fit, homogeneity, or independence? c) State your hypotheses. d) Check the conditions. e) How many degrees of freedom are there? f) Find x2 and the P-value. g) State your conclusion.

Week 13: 2-Variable Inferential Statistics 29 November 2016 Basic Statistics for Research Professor HK Dong Wendy Liu Hypothesis Testing Errors H 0rue H 0alse Do not reject H0 No error (1-α) Type II error (β) Reject H0 Type I error (α) No error (1-β α – amount of risk that we reject0H that is true 1-α – confidence coefficient – amount of confidence we have that the 0 is true when not rejected 2-population tests Mean o Z test – independent samples o T test – independent samples o Paired t test – paired/matched samples Proportion o Z test Variance o F test