(a) Find a point estimate of μ1 – μ2. Is the estimate biased or unbiased? (b) Find the estimated standard error the point estimate of μ1 – μ2? (c) Formulate and test the appropriate hypothesis at the α = 0.05 level.
Consider that μ1 and μ2 are the true mean stopping distances for motorcycles at 30 mph equipped with two different sets of tires.
Tire set 1 is more expensive, so we only want to buy them if there is strong evidence that there is a mean stopping distance of at least 3 ft shorter at 30 mph.
For Tire set 1, after nine tests, we get an x-bar1 of 110 ft and an s1 of 5 ft.
For Tire set 2, after eight tests, we get an x-bar2 of 120 ft and an s2 of 6 ft.
Assume that the distributions of stopping distances are roughly normal.
(a) Find a point estimate of μ1 – μ2. Is the estimate biased or unbiased?
(b) Find the estimated standard error the point estimate of μ1 – μ2?
(c) Formulate and test the appropriate hypothesis at the α = 0.05 level.
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