Question

Suppose μ₁ and μ₂ are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. Use the two-sample t test at significance level 0.01 to test H₀: μ₁ − μ₂ = −10 versus H_a: μ₁ − μ₂ < −10 for the following data: m = 6, x = 114.5, s₁ = 5.01, n = 6, y = 129.2, and s₂ = 5.32.

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t=

p-value=

Answer 1

The test statistic t = ((x - y) - ())/sqrt(s1^2/m + s2^2/n)

= (114.5 - 129.2 + 10)/sqrt((5.01)^2/6 + (5.32)^2/6) = -1.58

Df = (s1^2/m + s2^2/n)^2/((s1^2/m)^2/(m - 1) + (s2^2/n)^2/(n - 1))

= ((5.01)^2/6 + (5.32)^2/6)^2/(((5.01)^2/6)^2/5 + ((5.32)^2/6)^2/5) = 10

P-value = P(T < -1.58)

= 0.073