Each algorithm is applied to a group of 52 sample problems. The new algorithm completes the sample problems with a mean time of 24.04 hours. The current algorithm completes the sample problems with a mean time of 24.52 hours. The standard deviation is found to be 5.769 hours for the new algorithm, and 5.556 hours for the current algorithm. Conduct a hypothesis test at the 0.05 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm.

Therefore we fail to reject the Null hypothesis

Because the is no sufficient evidence to support the claim of the alternative hypothesis

Step-by-step explanation:

From the question we are told that

Sample size

Mean time 1

Mean time 2

Standard deviation

Standard deviation

Level of significance 0.05

The null hypothesis is

Alternative hypothesis

Generally the test statistics is mathematically represented as

From Table the Z-critical value at

Therefore

Zcal> Zcritical

(-0.43)=(-1.645)

Generally we fail to reject the null hypothesis at

Therefore we fail to reject the

Because the is no sufficient evidence to support the claim of

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18