Download Chapter 11 Exercises File

Study Questions on Ch.11
1) An induatrial engineer at the Lyons Products would like to determine whether
there are more units produced on the night shift than on the day shift. Assume the
population standard deviation for the number of units produced on the day shift is
21 and is 28 on the night shift. A sample of 54 day-shift workers showed that the
mean number of units produced on the day shift was 345. A sample of 60 nightshift workers showed that the mean number of units produced on the day shift was
351. At the 0.05 significance level, is the number of units produced on the night
shift larger?
Answer:
Step 1: Ho: 1  2
H1: 1 < 2
Step 2:   0.05
Step 4:
z
(Note: 1 represents day shift and 2 represents night shift)
Step 3 : Reject Ho if z < 1.65
345  351
(21) 2 (28) 2

54
60
 1.30
Step 5: Fail to reject Ho. There is not enough evidence to conclude that more units are
produced on the afternoon shift.
2) Each month the National Association of Purchasing Managers publishes the
NAPM index. One of the questions asked on the survey to purchasing agents is:
Do you think the economy is contracting? Last month, out of 300 responders 160
answered “yes” to the question. This month 170 of the 290 said the economy was
contracting. At the 0.05 significance level can we conclude that a larger
proportion of the agents believe the economy is contracting this month?
Answer:
Step 1: Ho: 1  2
H1: 1 < 2
Step 2:   0.05
(Note: 1 is for last month and 2 is for this month)
Step 3: If z < 1.65, reject Ho.
Step 4:
pc 
160  170
 0.56
300  290
z
0.5333  0.5862
 1.29
(0.56)(0.44) (0.56)(0.44)

300
290
Step 5: Do not reject the null. We cannot conclude an increased proportion believe the
economy is contracting.
3) The owner of King Burger wants to compare the sales per day at two locations.
The mean number sold for 10 randomly selected days at Kyrenia branch was
83.55 and the sample standard deviation was 10.50. For a random sample of 12
days at Famagusta branch, the mean number sold was 78.80 and the standard
deviation was 14.25. At the 0.05 significance level, is there a difference in the
mean number of hamburgers sold at the two branches?
Answer:
Step 1: Ho: n = s
H1: n  s
Step 3: df  n1  n2  2  10  12  2  20
critical t value: 2.086. So, reject null hypothesis if
if computed t is less than -2.086 or if greater than 2.086
Step 2:   0.05
Step 4:
2
2
(10  1)(10.5) 2  (12  1)(14.25) 2
2 ( n1  1) s1  ( n2  1) s 2
sp

 161.3
n1  n2  2
20
t
X1  X 2

83.55  78.8

4.75
 0.873
5.438
1
1
1
1
 )
161.3  
n1 n2
 10 12 
Step 5: Cannot reject null hypothesis and conclude there is no evidence that sales at two
locations are different.
s 2p (