- Fred is a new employee in a delicatessen. He is asked to cut cheese into 100 g blocks. A random sample of 8 of these blocks of cheese is selected. The weight, in grams, of each block of cheese is given below
$$94 , \quad 106 , \quad 115 , \quad 98 , \quad 111 , \quad 104 , \quad 113 , \quad 102$$
- Calculate a \(90 \%\) confidence interval for the standard deviation of the weights of the blocks of cheese cut by Fred.
Given that the weights of the blocks of cheese are independent,
- state what further assumption is necessary for this confidence interval to be valid.
The delicatessen manager expects the standard deviation of the weights of the blocks of cheese cut by an employee to be less than 5 g. Any employee who does not achieve this target is given training.
- Use your answer from part (a) to comment on Fred's results.
A second employee, Olga, has just been given training. Olga is asked to cut cheese into 100 g blocks. A random sample of 20 of these blocks of cheese is selected. The weight of each block of cheese, \(x\) grams, is recorded and the results are summarised below.
$$\bar { x } = 102.6 \quad s ^ { 2 } = 19.4$$
Given that the assumption in part (b) is also valid in this case,
- test, at a \(10 \%\) level of significance, whether or not the mean weight of the blocks of cheese cut by Olga after her training is 100 g . State your hypotheses clearly.
(6)