Q2.(6 pts) A die has 5 faces; two faces marked \'1\' and other three faces marke

Question

Q2.(6 pts) A die has 5 faces; two faces marked '1' and other three faces marked as '2'. Each throw, the number facedown the table is recorded. The test is to throw this die 40 times. Please answer the following questions. (Chi-square test) (1) Find the degree of freedom (2) Glve a table to list the observed and expected values of '1' and "2 (3) what is the critical value of the 95% confidence? (4) What is the number range of '1' and '2' to qualify this die be a fair one in this test (ist the result)?

Explanation / Answer

Q.2

The die is 5 face die. Two faces marked '1' and other three marks '2'

Number of throws = 40

(a) Degree of freedom = 2-1 = 1

(b) Expected number of 1's = (2/5) * 40 = 16

Expected number of 2's = (3/5) * 40 = 24

(3) Here critical value of the 95% confidence for dF = 1 and alpha = 0.05

X2critical = 3.8415

so X2 > X2critical we will reject the null hypothesis

Here X2 = (a-16)2 [1/16 + 1/24] > 3.8415

(a-16)2 (0.104167) > 3.8415

(a-16)2 > 36.8784

a - 16 > 6.0727 & 16 - a > 6.0727

a > 22.0727 and a < 9.927

so any values of 1's in between 10 to 22 would qualify that die is a fair one for this test.

Value observed (O) expected (E) (O-E)^2/E 1 a 16 (a - 16)^2/16 2 40-a 24 (a - 16)^2/24

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