A quality controller at a beverage manufacturer is concernedthat a bottling machine is under-filling (an opaque container) thatis supposed to contain 1000 mL of fluid. A random sample of 20containers is therefore taken and the volume in each recorded inthe file STA201 201960 Assn Bottles.xlsx. In researching theproblem the quality controller sees a statement in the machine’smanual that “volumes dispensed by the machine will follow a normaldistribution”. (a) Based on the information provided, write downthe null and alternate hypothesis that the quality controllershould employ to test this concern. (b) Say why thestatement in the manual is important to this analysis and thenwrite down the name of the test to be employed. (c) Writedown the decision rule in terms of a test statistic and give thecorresponding decision rule using a p value. Note: Use a 5% levelof significance for the test. (d) Calculate the value ofthe test statistic manually. (e) State whether you rejectthe null hypotheses or otherwise, justify your decision and thendraw a conclusion that answers the original question.
Bottle | Volume |
1 | 968.22 |
2 | 918.98 |
3 | 942.76 |
4 | 1024.02 |
5 | 988.96 |
6 | 1057.26 |
7 | 987.28 |
8 | 970.06 |
9 | 947.76 |
10 | 1003.18 |
11 | 1005.7 |
12 | 1076.16 |
13 | 931.36 |
14 | 990.06 |
15 | 950.64 |
16 | 1058.82 |
17 | 1036.26 |
18 | 928.64 |
19 | 898.16 |
20 | 978.54 |
