Problem 6 The power of this test against the alternative hypothesis that the chance the die lands with two spots showing is 32.45%, the chance the die lands with five spots showing is 0.88%, and the chances the die lands with one, three, four, or six spots showing each equal 1/6, is (Q9)Problem 3 Under the null hypothesis, the expected number of times the die lands showing one spot is (Q5) 5 and the standard error of the number of times the die lands showing one spot is (Q6) 0.3726 Problem 4 The significance level of this test is (Q7) 0.05 I Problem 5 The power of this test against the alternative hypothesis that the chance the die lands with one spot showing is 10.43%, the chance the die lands with six spots showing is 22.9%, and the chances the die lands with two, three, four, or five spots showing each equal 1/6, is (Q8)Problem 2 Under the null hypothesis, the distribution of the number of times the die lands showing one spot is (Q3) binomial with parameters (Q4) n=30, p=1/6 ? N=30, G=6, n=5 p=1/6, r=1 p=1/6 thesis, the expected number of times the die lands showing mean=6, SD=2.041 and the standard error of the number of times n=30, p=1/6 ig one spot is (Q6) 0.3726 none of the aboveAn experimenter suspects that a certain die is "loaded;" that is, the chances that the die lands on different faces are not all equal. Recall that dice are made with the sum of the numbers of spots on opposite sides equal to 7: 1 and 6 are opposite each other, 2 and 5 are opposite each other, and 3 and 4 are opposite each other. The experimenter decides to test the null hypothesis that the die is fair against the alternative hypothesis that it is not fair, using the following test. The die will be rolled 30 times, independently. If the die lands with one spot showing 9 times or more, or 0 times, the null hypothesis will be rejected.Problem 2 Under the null hypothesis, the distribution of the number of times the die lands showing one spot is (Q3) binomial V with parameters (Q4) n=30, p=1/6 2 normal geometric Problem 3 negative binomial Under the null hypothesis binomial ber of times the die lands showing one spot is (Q5) 5 hypergeometric ard error of the number of times the die lands showing one 16 none of the above