# Chi Square test of Independence

1. In a study of store checkout scanning systems, samples of purchases were used to

compare the scanned process to the posted prices. The accompanying table

summaries results for a sample of 819 items.

Regular-priced

items Advertised-special

items

Undercharge 20 7

Overcharge 15 29

Correct price 384 364

a. Among the regular-priced items, what percentage are overcharged? Among advertised-special items, what percentage are overcharged? Compare the two results.

b. Identify the null and alternative hypotheses for a test of the claim that the two variables (charge and pricing) are independent.

c. Find the expected values for each cell by assuming that the charge (under, over, correct) is independent of the pricing (regular, advertised-special).

d. Find the value of the X^2 (Chi-square) statistic for a hypothesis test of the claim that the two variables (charge and pricing) are independent.

e. Based on the result from part d and the size of the table, refer to table 10.12 and determine what is known about the P-value.

f. Based on the preceding results, what can you conclude from the hypothesis test about whether the two variables (charge and pricing) are independent?

Table 10.12 Critical Values of X^2: reject H0

Only if X^2>Critical Value

Significance level

Table size 0.05 0.01

(rows X columns)

2x2 3.841 6.635

2x2 or 3x2 5.991 9.210

3x3 9.488 13.277

2x4 or 4x2 7.815 11.345

2x5 or 5x2 9.488 13.277

See attached file for full problem description

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#### Solution Summary

The solution gives step by step procedure for the computation of Chi Square test of Independence. Null hypothesis, alternative hypothesis, test statistic, critical Value and p value are also included in the solution.