Question

Question 3:

An engineer is designing a kayak that holds a single person together with a bag. It is known that kayak users have a mean (person) weight of ?₁= 78 and a standard deviation of ?₁= 12.3 (all units in kilograms). Denote the (unknown) population mean and population standard deviation of bag weights, by ? ₂ and ?₂ respectively.

The engineer measures bags of 16 randomly selected users. A sample mean of x = 25.2 and a sample standard deviation of s = 4.2 are obtained.

(a) Find a 99% confidence interval for ? ₂. State your assumptions on the population of bags.

(b) Previous manufacturers have assumed a bag weight of 30. However, the data collected indicate a potentially lower weight. Hence, the engineer wishes to claim that bag weight assumptions were too conservative. She decides to test the hypothesis, H0 : ? ₂ = 30 vs. H1 : ? ₂ < 30, setting ?  = 10%. What does the engineer conclude? Carry out the hypothesis test.

(c)At this point, the engineer assumes that ?₂ = 25.2 and ?₂ = 4.2. She further assumes that person weights are independent of bag weights and that all weights are Normally distributed. To what weight capacity (person + bag) should the engineer design the Kayak to accommodate 99% of the users? Show your working.

Answer 1