Answer:
Step-by-step explanation:
This is a test of 2 independent groups. The population standard deviations are not known. it is a two-tailed test. Let μ1 be the true mean completion time for the new algorithm and μ2 be the true mean completion time for the current algorithm.
The random variable is μ1 - μ2 = difference in the mean completion time between the new algorithm and the current algorithm.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 ≤ μ2 H0 : μ1 - μ2 ≤ 0
The alternative hypothesis is
H1 : μ1 > μ2 H1 : μ1 - μ2 > 0
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(μ1 - μ2)/√(s1²/n1 + s2²/n2)
From the information given,
μ1 = 19.15
μ2 = 22.01
s1 = 5.784
s2 = 4.293
n1 = 53
n2 = 53
t = (19.15 - 22.01)/√(5.784²/53 + 4.293²/53)
t = - 2.89
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [5.784²/53 + 4.293²/53]²/[(1/53 - 1)(5.784²/53)² + (1/53 - 1)(4.293²/53)²] = 0.958/0.0099876314
df = 100
We would determine the probability value from the t test calculator. It becomes
p value = 0.0023
Since alpha, 0.05 > than the p value, 0.0023, then we would reject the null hypothesis.
