Respuesta :
Answer:
B. Fail to reject null hypothesis .
Step-by-step explanation:
We are given that a systems analyst tests a new algorithm designed to work faster than the currently-used algorithm.
Also, [tex]\mu_1[/tex] = true mean completion time for the new algorithm
[tex]\mu_2[/tex] = true mean completion time for the current algorithm
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 = \mu_2[/tex] {Both new and current algorithm has same
completion time}
Alternate Hypothesis, [tex]H_1[/tex] : [tex]\mu_1 < \mu_2[/tex] {New algorithm has lower mean
completion time than current algorithm}
The test statistics we use here will be :
[tex]\frac{(X_1bar - X_2bar)- (\mu_1 - \mu_2)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }[/tex] follows [tex]t_n__1 + n_2-2[/tex]
where, [tex]X_1bar[/tex] = 18.78 hours and [tex]X_2bar[/tex] = 19.06 hours
[tex]s_1[/tex] = 5.614 hours and [tex]s_2[/tex] = 5.012 hours
[tex]n_1[/tex] = 46 and [tex]n_2[/tex] = 46
[tex]s_p = \sqrt{\frac{(n_1-1)s_1^{2} + (n_2-1)s_2^{2} }{n_1 + n_2 - 2} }[/tex] = 5.321
Here, we use t test statistics because we know nothing about population standard deviations.
Test statistics = [tex]\frac{(18.78 - 19.06)- 0}{5.321\sqrt{\frac{1}{46}+\frac{1}{46} } }[/tex] follows [tex]t_9_0[/tex]
= -0.2524
At 0.1 or 10% level of significance t table gives a critical value between -1.296 and -1.289 at 90 degree of freedom. Since our test statistics is more than the critical table value of t as -0.2524 > -1.296 to -1.289 so we have insufficient evidence to reject null hypothesis.
Therefore, we conclude that new algorithm has same mean completion time with that of current algorithm.
