Problem 2: An automotive manufacturer wants to reduce the weight of gearboxes to increase fuel efficiency. The research department used a different than regular material to produce 20 gearboxes as a sample. They found that the mean weight of these 20 gearboxes was 9.8 kg with a standard deviation of 0.025kg. The department then took a sample of 15 regularly produced gearboxes and found that their mean weight was 9.83 kg with a standard deviation of 0.023kg. a) Conduct an appropriate hypothesis test using the critical value method. Use the regularly produced gearboxes as population 1. (Assume unequal population variances.] [9 marks] b) Explain what a Type II Error will mean in this context. [1 mark]