Advanced High-School Mathematics

414 CHAPTER 6 Inferential Statistics

where, in this case,Awould be the cell counts in the above contingency
table. The TI-calculator will automatically generate from the matrix
Aa secondary matrix B consisting of the expected counts. Invoking
theχ^2 test using the matrix

A =







52 35 76 63

89 83 78 82

88 83 85 81







results in the output

χ^2 - Test

χ^2 = 13. 83966079

P=.0314794347

df=6.

Exercises

1. The TI commandrandInt(0,9) will randomly generate an integer
   (a “digit”) between 0 and 9. Having nothing better to do, we
   invoke this command 200 times, resulting in the table:

digit 0 1 2 3 4 5 6 7 8 9

frequency 17 21 15 19 25 27 19 23 18 17

We suspect that the commandrandIntought to generate random

digitsuniformly, leading to the null hypothesis

H 0 : pi=

1

10

, i= 0, 1 , 2 ,..., 9 ,

wherepi is the probability of generating digiti, i= 0, 1 , 2 ,..., 9.

Test this hypothesis against its negation at the 5% significance

level.

2.^33 Eggs at a farm are sold in boxes of six. Each egg is either brown
or white. The owner believes that the number of brown eggs in a

(^33) Adapted from IB Mathematics HL Examination, Nov 2003, Paper 2 (Statistics), #6 (iv).