Question

It is claimed that the mean repair cost for two models of washing machines are the same. The mean repair cost for a sample of 24 Model A machines is $212. The mean repair cost for a sample of 26 Model B machines is $221. Both populations are normally distributed. The population standard deviation of the Model A machines is $18 and the population standard deviation of the Model B machines is $22. Test the claim at the .05 significance level (α=.05). Use the traditional method. Include a bell-graph.

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 = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(324/24 + 484/26)
sp = 5.667

Test statistic,
z = (x1bar - x2bar)/sp
z = (212 - 221)/5.667
z = -1.59

fail to reject null hypothesis.

P-value Approach
P-value = 0.1118
As P-value >= 0.05, fail to reject null hypothesis.