Please do not use excel to solve and give your answers in 4 decimal places. Do all calculation manually.

QUESTION 1 [15 MARKS]

(a) Describe why hypothesis testing is performed. [2 Marks]

(b) Engineers of SY Spring Trading company who are in charge of the production of springs used to make car seats are concerned about the variability of the springs. The springs are designed to be 500 millimeter (mm) long. If the springs are too long, they will loosen and fall out and if the springs are too short, they will not fit into the frames. The springs that are too long and too short must be reworked at an additional cost. The engineers have calculated that a standard deviation of more than 2 mm will result in an acceptable number of springs that must be reworked. A random sample of 96 springs are measured and it is found that the length of the spring has variance of 6.7276.

i) Can we conclude that the number of springs requiring reworking is extremely large? [7 Marks]

ii) What is the required condition of the data for the method used in (i)? Then, suggest one method that can be used to check that required condition. [2 Marks]

iii) Based on your answer in (i), identify the type of error. Justify your answer. [2 Marks]

iv) Describe a possible effect to the SY Spring Trading based on your answer in (iii). What can the engineers suggest to the company? [2 Marks]