Question

Hoping to improve sales, one company decided to introduce more attractive packaging. To test the effec on sales, the manager distributes the new design to supermarket 1, while sending the old design to supermarket 2. The barcode data were recieved after a certain period. The code for this product was 9077 in both supermarkets. Since the cost for the new packaging is more expensive, the manager wants to know the effectiveness of this new design. The collected data for the total transactions (n) and the number of 9077 (x) is as follows:

Market 1--> n=904, x=180

Market 2--> n= 1038, x =155

i. What is the alternative hypothesis about this question?

ii. What is the pooled proportion? (p1-p2)?

iii. What is the standard error for (p1-p2)?

iv. What is the z-statistic for (p1-p2)?

v. What is the z-critical value?

vi. If our z-statistic is greater than zcritical then how should we conclude?

Because the new design is more expensive, the management requires the new design to outsell the old one by at least 2%.

vii. What is the standard error for (p1-p2)

viii. What is the z-statistic for (p1-p2)

Answer 1

(i) p^₁ = 180/904 = 0.1991

p^₂ = 155/1038 = 0.1493

Here alterntive Hypothesis is

H_a : p₁ > p₂

(ii) Pooled Proportion = (155 + 180)/(1038 + 904) = 0.1725

(iii) standard error of proportion = sqrt [0.1725 * (1 - 0.1725) * (1/1038 + 1/904)] = 0.0172

(iv) Z = (0.1991 - 0.1493)/0.0172 = 2.895

(v) Here Z(critical) = 1.96

(vi) Here we conclude that method new is better than method old.

(viii) here standard error will be same = 0.0172

(viiii)

Z = (0.1991 - 0.1493 - 0.02)/0.0172 = 1.7326