Question

a:)A representative visits Bob's Coffee and buys 9 coffees. They measure the bitterness using special equipment and find that average bitterness is 2.5. Bitterness in Bob's coffee is only supposed to be equal to 1. Assume that bitterness in each cup follows a normal distribution with some mean µ and variance σ 2 = 4. Test the hypothesis H₀ : µ = 1 versus the alternative H_a : µ does not equal 1 by computing the p-value. Would the hypothesis be rejected at the 5% significance level?

b:)Do the hypothesis test for Bob's Coffee again, but this time don’t assume we know the population variance σ 2 . The representative measures the sample variance s² = 4. You won’t be able to compute a p-value without a computer, but test the hypothesis at the 5% level by looking up the appropriate critical values.

Answer 1