Question

13. Most people have returned clothing or other items to stores. Acme holding company is particularly interested in the clothes that have been returned after the winter holidays. It requires its stores to keep records of these clothes if they cost over $75.00. Acme's corporate office is worried about a new store (N) it recently purchased. The store seems to have a high proportion of returns compared to an established store (E) in a similar neighborhood. After the last holiday season, store N had 162 returns of clothing items that cost over $75. In total store N sold 900 items. Store (E) had 60 returns that cost over $75 out of total sales of 750 items. Do these data provide sufficient evidence at the 0.05 level of significance to conclude that the new store has more returns than the established store? (Note...do this problem using new store (N) - established store (E).) (30 points.) a. State the null and alternative hypotheses.

Answer 1

Given that

For store N

Total number of shopping =n1=900

Number of returns=x1=162

For store E

Total number of shopping =n2=750

Number of returns =x2=60

a)

We have to test the claim that "new store(N) have more return than that of established(E) store"

We can test that claim by testing that proportions of returns at store N is greater proportion of returns at the store E

Let proportion of returns at N is denoted by P1

Proportion of returns at E is denoted by P2 so

H0: P1-P2=0

H1:P1-P2>0

b)

Since we are testing that if P1 is greater than P2 or not so

It's right tailed test

c)

Sample proportions are given by

h_xl_162 = 0.18, B2 = -35 = 750 = 0 P1 = n1 900 _22_60 00=0.08

d)

Now pooled proportion is given by

Ppooled = 1 + x2 162 + 60 nl + n2900 + 750 = 0.1345

e)

Standard error of difference of proportion is given by

f)

29100 -1002(Gtel 0 – 1) stevo pod 1) a poule 1 = as

P-P = 0.18 – 0.08 = 0.10

g)

B1-B2 0.10 SE =00167 = 5.988

h)

Yes value of test statistics is un usual as most of Z scores lies below the 4 while it's around 6

i)

P value =P(Z>5.988)<0.001

In graph we can show it in right tail

j)

Since P value is less than level of significance hence we reject H0

k)

There are enough evidence to support the claim that returns at store N are greater than that at E