Question

Two microprocessors are compared on a sample of six benchmark codes to determine whether there is a difference in speed. The times (in seconds) used by each processor on each code are given in the following table.

                                                                  Code                                           

                           1              2               3              4             5             6

Processor A    27.2         18.1           27.2         19.7        24.5        22.1

Processor B     24.1         19.3           26.8         20.1        27.6       29.8

1. Can you conclude that the mean speeds of the two processors differ?
2. Verify your result in part a) using the appropriate confidence interval.

Answer 1

using minitab>stat>basic stat>two sample t

we have

Two-Sample T-Test and CI: processor A, Processor B

Two-sample T for processor A vs Processor B

N Mean StDev SE Mean
processor A 6 23.13 3.82 1.6
Processor B 6 24.62 4.23 1.7

Difference = μ (processor A) - μ (Processor B)
Estimate for difference: -1.48
95% CI for difference: (-6.67, 3.70)
T-Test of difference = 0 (vs ≠): T-Value = -0.64 P-Value = 0.538 DF = 10
Both use Pooled StDev = 4.0324

the null and alternative hypothesis is

H0:μ (processor A) = μ (Processor B)

Ha:μ (processor A) μ (Processor B)

a ) No , we cannot   conclude that the mean speeds of the two processors differ because p value of test statistic is 0.538 which is greater then 0.05

b ) 95% CI for difference: (-6.67, 3.70)

since the 95% confidence interval contain 0 so we do not reject Ho and

so we  cannot  conclude that the mean speeds of the two processors differ