Question

. A major keyboard manufacturer has a line of keyboards designed for apartment dwellers. These keyboards need to be light enough to be carried up flights of stairs. The lead engineer wants to use a new type of material. The engineer claims that the new keyboards will be lighter than the old keyboards. They take a sample of 4 keyboards manufactured using the old material and compute an average weight of 21 kg with a standard deviation of 1 kg. They take a sample of 8 keyboards manufactured using the new material and compute an average weight of 17 kg with a standard deviation of 2 kg. a. Conduct an appropriate hypothesis test using the p-value method. Use the old material as population 1. [8 marks] b. How much evidence is there against the null hypothesis in part (a)? [1 mark] c. Explain what a Type II Error means in this context. [1 mark] PLEASE USE THE WELCHS METHOD (unequal variances procedure)

Answer 1

(a)

(b)

P-value is very small so it shows a strong evidence against the null hypothesis.

(c)

Type II error is the probability of rejecting the false null hypothesis.

That is researcher incorrectly conclude that new keyboards is lighter than the old keyboards while actually new keyboards is not lighter than the old keyboards.