These data are obtained on the cpu time required to solve an algorithm: 2.0 1.4

Question

These data are obtained on the cpu time required to solve an algorithm:

2.0 1.4 3.5 2.3 3.2 3.6 .1 3.5 2.2 2.1 2.4 1.5 2.2 2.3 2.7 1.9 1.7 1.8 3.1 1.5 1.5 2.6 2.8 2.5 2.5 3.9 .8 1.8 3.3 3.7

a. Estimate the mean and standard deviation.

b. Find a 99% confidence interval on the mean time required to solve a problem

c. Another algorithm takes an average of 6.6 cpu time. The solutions obtained are equivalent. Does the new algorithm appear to be more efficient than the other with respect to computing time? Explain

Explanation / Answer

From this data, we calculate mean: 2.34667 std dev:: 0.891621 n:30

c. Since 6.6 is on right it this CI, yes the new algorithm is faster than other with respect to computing time.

Sample Mean = 2.34667
SD = 0.891621
Sample Size (n) = 30
Standard Error (SE) = SD/root(n) = 0.1628
alpha (a) = 1-0.99 = 0.01
we use t-distribution as population standard deviation is unknown
t(a/2, n-1 ) = 2.7564
Margin of Error (ME) = t(a/2,n-1)x SE = 0.4487

99% confidence interval is given by:
Sample Mean +/- (Margin of Error)
2.34667 +/- 0.4487 = (1.8979 , 2.7954)

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