Question

	New	Current
Sample Size	10	10
Sample Mean	542.0000	570.5000
Sample Standard Deviation	38.1663	32.2706
df
Pooled Sample Standard Deviation	35.3416
Confidence Interval (in terms of New - Current)
Confidence Coefficient	0.90
Lower Limit
Upper Limit
Hypothesis Test (in terms of New - Current)
Hypothesized Value
Test Statistic
p-value (Lower Tail)	0.0441
p-value (Upper Tail)
p-value (Two Tail)

	New	Current
Sample Size	10	10
Sample Mean	542.0000	570.5000
Sample Standard Deviation	38.1663	32.2706
df	17
Confidence Interval (in terms of New - Current)
Confidence Coefficient	0.90
Lower Limit
Upper Limit
Hypothesis Test (in terms of New - Current)
Hypothesized Value
Test Statistic
p-value (Lower Tail)	0.0446
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 10 projects that used the current technology and 10 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=.01? Based on this paragraph of text, use the correct excel output above to answer the following question.

For the hypothesis stated above, what is the decision rule?

	a.	Reject H0 if the test statistic is less than -2.898 or greater than 2.898.
	b.	Reject H0 if the test statistic is less than -2.575 or greater than 2.575.
	c.	Reject H0 if the test statistic is less than -2.878 or greater than 2.878.
	d.	Reject H0 if the test statistic is less than -2.552 or greater than 2.552.
	e.	None of the answers is correct

Answer 1

The test statistic under th enull hypothesis is:

Using the information given in the tables we get:

sp = 35.3416

t = 1.8032

The critical value of t for 18 degrees of freedom is and 1% level of significance is 2.878.

Since, the t-statistic is less than the critical value of t, we may accpet the null hypothesis at 1% level of significance and conclude that the completion time for the project may be the same with both the current and the new technology,

The decision rule is:

Reject H0 if the test statistic is less than -2.878 or greater than 2.878.