Question

A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 54 sample problems. The new algorithm completes the sample problems with a mean time of 19.20 hours. The current algorithm completes the sample problems with a mean time of 21.49 hours. Assume the population standard deviation for the new algorithm is 3.259 hours, while the current algorithm has a population standard deviation of 3.804 hours. Conduct a hypothesis test at the 0.1 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Let μ1 be the true mean completion time for the new algorithm and μ2 be the true mean completion time for the current algorithm. Step 3 of 5 : Find the p-value associated with the test statistic. Round your answer to four decimal places.

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 = 0.1
Critical value of z is -1.282.
Hence reject H0 if z < -1.282

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(10.621081/54 + 14.470416/54)
sp = 0.6817

Test statistic,
z = (x1bar - x2bar)/sp
z = (19.2 - 21.49)/0.6817
z = -3.36

P-value Approach
P-value = 0
As P-value >= 0.1, fail to reject null hypothesis.