BUSI
1013:
S
TATISTICS FOR
B
USINESS
9
Twosample
z
interval for
p
1

p
2
Why?
To locate the difference between two population proportions
p
1

p
2
.
When?
Under the same conditions as for the
z
test listed above.
How:
2
2
2
1
1
1
2
1
ˆ
1
ˆ
ˆ
1
ˆ
ˆ
ˆ
n
p
p
n
p
p
z
p
p
c
where
c
z
is the critical value from the standard normal distribution corresponding to level
C
confidence.
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
BUSI
1013:
S
TATISTICS FOR
B
USINESS
10
Now, our week assignment:
1.
Waiting time at checkout lines for two stores of a supermarket chain were measured
for a random sample of customers at each store. The chain wants to use this data to
test the research (alternative) hypothesis that the mean waiting time for checkout at
Store 1 is lower than that of Store 2. (
12 points
)
Store 1 (in Seconds)
Store 2 (in Seconds)
470
375
394
319
167
266
293
324
187
244
115
178
195
279
400
289
228
342
315
212
195
188
a. What are the null and alternative hypothesis for this research?
BUSI
1013:
S
TATISTICS FOR
B
USINESS
11
b. What are the sample mean waiting time at checkout lines and the sample
standard deviation for the two stores?
c. Compute the test statistic t used to test the hypothesis. Note that the
population standard deviations are not known and therefore you cannot
use the formula in Section 10.1. Use the one in Section 10.2 instead.
d. Compute the degree of freedom for the test statistic t.
e. Can the chain conclude that the mean waiting time at Store 1 is lower than
that of Store 2? Use the criticalvalue approach and
α
= 0.05 to conduct
the hypothesis test.
Since t = 0.551 is not less than 1.74 or 1.734, do not reject H
0
The chain cannot conclude that the mean waiting time at Store 1 is
lower than that of Store 2
f.
Construct a 95% confidence interval for the difference of mean waiting
time at checkout lines for the two stores.
BUSI
1013:
S
TATISTICS FOR
B
USINESS
12