Question

	New	Current
Sample Size	8	8
Sample Mean	558.7500	604.3750
Sample Standard Deviation	49.1899	44.5162
df
Pooled Sample Standard Deviation	46.9113
Confidence Interval (in terms of New - Current)
Confidence Coefficient	0.99
Lower Limit
Upper Limit
Hypothesis Test (in terms of New - Current)
Hypothesized Value
Test Statistic
p-value (Lower Tail)	0.0361
p-value (Upper Tail)
p-value (Two Tail)

	New	Current
Sample Size	8	8
Sample Mean	558.7500	604.3750
Sample Standard Deviation	49.1899	44.5162
df	13
Confidence Interval (in terms of New - Current)
Confidence Coefficient	0.99
Lower Limit
Upper Limit
Hypothesis Test (in terms of New - Current)
Hypothesized Value
Test Statistic
p-value (Lower Tail)	0.0369
p-value (Upper Tail)
p-value (Two Tail)

IBM is interested in comparing the average systems analyst project completion time using the current technology and using the new computer software package. So, a statistical consultant for IBM randomly selected 8 projects that used the current technology and 8 projects that used the new computer software package. The completion time (in hours) for each project was recorded and then entered into Excel. Assume the samples are independent and from normal populations with equal variances. Can IBM reject the hypothesis μ_New - μ_Current = 0 at α=.05? Based on this paragraph of text, use the correct excel output above to answer the following question.

What is the 99% confidence interval for μ_Current - μ_New?

	a.	(-25.0234, 116.2734)
	b.	(-39.5990, 130.8490)
	c.	(-4.6874, 95.9374)
	d.	None of the answers is correct
	e.	(-24.2025, 115.4525)

Answer 1

The given interval is as:

-0.06436 < p1-p2 < 0.10778

sp = sqrt((((n1 - 1)*s1^2 + (n2 - 1)*s2^2)/(n1 + n2 - 2))*(1/n1 + 1/n2))
sp = sqrt((((8 - 1)*44.5162^2 + (8 - 1)*49.1899^2)/(8 + 8 - 2))*(1/8 + 1/8))
sp = 23.4556

Given CI level is 0.99, hence α = 1 - 0.99 = 0.01                  
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 2.977                  
                  
Margin of Error                  
ME = tc * sp                  
ME = 2.977 * 23.4556                  
ME = 69.827                  
                  
CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)                  
CI = (604.375 - 558.75 - 2.977 * 23.4556 , 604.375 - 558.75 - 2.977 * 23.4556                  
CI = (-24.2025 , 115.4525)

Option e)