Question

015824 A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 89 sample problems. The new algorithm completes the sample problems with a mean time of 17.64 hours. The current algorithm completes the sample problems with a mean time of 17.75 hours. Assume the population standard deviation for the new algorithm is 4.561 hours, while the current algorithm has a population standard deviation of 4.210 hours. 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. 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 1 of 5: State the null and alternative hypotheses for the test.

Answer 1

:  the true mean completion time for the new algorithm

:  the true mean completion time for the current algorithm

The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge.

The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.

Claim : the new algorithm has a lower mean completion time than the current algorithm.

Step1 of 5:

Null hypothesis : H_o:  True mean completion time for the  new algorithm =True mean completion time for the  current algorithm : = or - = 0

Alternate Hypothesis :H_a: True mean completion time for the  new algorithm < True mean completion time for the  current algorithm: (Left tailed test)

< or   - < 0

Null hypothesis : H_o: - = 0

Altrenate Hypothesis : H_a : - < 0

Test Statistic when population standard deviations are known:

Given
n1: Sample Size of New Algorithm	89
n2 : Sample Size of Current Algorithm	89
: Sample Mean time of New Algorithm	17.64
: Sample Mean time of Current Algorithm	17.75
: Population Standard Deviation of New Algorithm	4.561
: Population Standard Deviation of current Algorithm	4.21
Level of Significance :	0.05

For Left Tailed Test : Reject null hypothesis if Calculated value of Z is less than Critical Value ;Z

As Calculated Value of Z is greater than Critical Value i.e. ( -0.1672>-1.6449 ); Fail To Reject Null Hypothesis

Not enough evidence to reject null hypothesis;

There is no significant difference in the mean completion times between the new algorithm and current algorithm.

Reject the claim.