Question

To compare two kinds of bumper guards, six of each kind were mounted on a car. Then the car was run into a concrete wall. Statistics for the costs of repairs are: ¯x1 = 140, ¯x2 = 149,

(s1)^2 = 80,

(s2) ^2 = 82.

Assume that the two populations are normal, independent and have the same variance. Test at α = .01 the null hypothesis that there is no difference between costs of repairs.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 ≠ μ2

Rejection Region
This is two tailed test, for α = 0.01 and df = n1 + n2 - 2 = 10
Critical value of t are -3.169 and 3.169.
Hence reject H0 if t < -3.169 or t > 3.169

Pooled Variance
sp = sqrt((((n1 - 1)*s1^2 + (n2 - 1)*s2^2)/(n1 + n2 - 2))*(1/n1 + 1/n2))
sp = sqrt((((6 - 1)*8.9443^2 + (6 - 1)*9.0554^2)/(6 + 6 - 2))*(1/6 + 1/6))
sp = 5.1962

Test statistic,
t = (x1bar - x2bar)/sp
t = (140 - 149)/5.1962
t = -1.732

P-value Approach
P-value = 0.1139
As P-value >= 0.01, fail to reject null hypothesis.