Bottle Company Part 1

BottleCompany

Part 1

Bottle Number

Ounces

1

14.23

2

14.32

3

14.98

4

15

5

15.11

6

15.21

7

15.42

8

15.47

9

15.65

10

15.74

11

15.77

12

15.8

13

15.82

14

15.87

15

15.98

16

16

17

16.02

18

16.05

19

16.21

20

16.21

21

16.23

22

16.25

23

16.31

24

16.32

25

16.34

26

16.46

27

16.47

28

16.51

29

16.91

30

16.96

Mean

15.854

Median

15.99

Std Dev

0.661381

Part 2

Since n ≥ 30 the confidence interval can be obtained using the z-distribution and the formula for 95% confidence as follows:

n =

30

15.854

s =

0.661381

15.854

+

1.96 x

0.661381

30

15.854

+

0.2367

16.0907

or

15.6173

Part 3

We check if the mean is less than the 16 ounces (we select =0.05)

n =

30

15.854

s =

0.661381

We use the z-statistics since the number is less than 30

Z =

15.854

16

0.661381

=

-1.209

Decision

Since the statistic value is -1.209 is higher than -1.645 we reject both hypothesis

We are in case b)this is because in the test above we concluded that the mean exceeds 16

Possible explanations

The machine is malfunctioning thus filling a bottle takes too long. A bottling plant has several machines. The company probably employs a filler to put the beverage into the bottle. The filler may malfunction due to some reasons. It may be faulty due to wear and tear or as a result of poor calibration. It is advisable that the management checks the calibrations of this machine and to service the machine so as to ascertain why bottle filling takes a long time which could be the cause of the too much soda ending up in the bottle.

The line system is not working correctly, for example, line speed is low which causes the bottle to have excess beverage The slow line speed will affect the company significantly since it also reduces the rate of production. The company’s output may fall below optimal levels because it will take longer than before to produce a given number of products. The line speed should be examined by a machine specialist to ascertain the cause of the problem early enough. Management should have a policy of servicing these machines periodically.

The bottles are not good enough, for example, the top of the bottles are big, and thus too much of the soda goes into the bottle. Bottling companies either create new bottles with each new batch of a product produced or recycle previously used bottles. If they recycle, they obtain the used bottles from the market, clean them and fix new seals or bottle tops. If this company uses this method, then it is unlikely that the bottles are the cause of the problem. Some bottling companies have a part of the plant that specializes in making bottles. That part usually has a mold which acts as a template or stencil for creating new bottles. If the company uses this approach, it should re-examine its molds to see if their size changed. A change in size could result in the production of bigger, poorly shaped bottles which could contribute to the problem. Repair of the molding system may rectify the problem. If the company creates a servicing policy to ensure the machines in the various department undergo checks regularly, it will be very easy to detect anomalies in the production process before they spill over to the final consumer.