Question

Chapter 4, Section 2, Exercise 079 Thirty students are asked to choose a random number between 0 and 9, inclusive, to create a data set of n 30 digits. If the numbers are truly random, we would expect about 3 zeros, 3 ones, 3 twos, and so on. If the data set includes 8 sevens, how unusual is that? If we look exclusively at the number of sevens, we expect the proportion of sevens to be 0.1 (since there are 10 possible numbers) and the number of sevens to be 3 in a sample size of 30. we are testing Ho : p = 0.1 vs Ha : pヂ0.1 where p is the proportion of sevens. We can generate the randomization distribution by generating 1000 sets of 30 random digits and recording X = the number of sevens in each simulated sample. See the figure below What is your lucky number 250 229 227 200 183 150 136 106 100 50 50 47 16 Sevens (a) Notice that this randomization distribution is not symmetric. This is a two-tailed test, so we need to consider both "tails". How far is X-9 from the expected value of 3? What number would be equally far out on the other side? (a) Notice that this randomization distribution is not symmetric. This is a two-tailed test, so we need to consider both "tails. How far is X -9 from the expected value of 3? What number would be equally far out on the other side? the expected value of 3 would be equally far out on the other side (b) What is the p-value for the observed statistic of X-8 sevens when doing the two-tail test? -value- (c) The randomization distribution in the above figure would apply to any digits (not just sevens) if the null hypothesis is H0 : p = 0.1 . Suppose we want to test if students tend to avoid choosing zero when picking a random digit. If we now let p be the proportion of zeros all students choose, the alternative would be Ha P

Answer 1

ANS ::-

AS FOR GIVEN DATA...

(A)

X=8 is -1 (2-3) above the expected value of 3.

0 would be equally for out on the other side.

(B)

The observed static of X=8 seven is 2+1 =3 of the 1000 simulation. Notice that this randomization distribution is not symmetric. This is a two-tailed test, so we need to consider both “tails”. The p-value for a two-tailed test is double of a one-tail test.

Hence,  p-value for a two-tailed test = 2(3/1000) = 0.006

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