Question

The TDI conducts a test on fairness of premiums charged by companies 1 and 2. It is known that population variances are σ^2 1 = 270 and σ^2 2 = 480. 30 premiums charged by each company yielded sample means 384 and 396.5, respectively. (a) Test at α = .02 the hypothesis that the population mean premiums are the same versus that the second company charges more. (b) Calculate p-value and make a conclusion about correctness of your decision in part (a).

Answer 1

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

Rejection Region
This is left tailed test, for α = 0.02
Critical value of z is -2.054.
Hence reject H0 if z < -2.054

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(270.00076489/30 + 480/30)
sp = 5

Test statistic,
z = (x1bar - x2bar)/sp
z = (384 - 396.5)/5
z = -2.5

fail to reject null hypothesis.

b)

P-value Approach
P-value = 0.0060
As P-value >= 0.02, fail to reject null hypothesis.