John Smith, Director of the NJ Nonprofits Working Group, is interested in the emerging trend of small nonprofits (defined as those with budgets less than $2 million per year) collaborating with each other for the purpose of sharing administrative services (e.g., accounting, human resources). Mr. Smith hypothesizes that nonprofits engaged in collaborative relationships should be able to spend less on administrative services than nonprofits not engaged in collaborative cost-sharing agreements. To test this hypothesis, Mr. Smith collects data for a random sample of 150 small nonprofits in the state. Specifically, the variable of interest is the percentage of each organization’s annual budget spent on administrative services. In the sample, 75 of these organizations are engaged in collaborative cost-sharing agreements (“SHARE” group), and the other 75 are not (“NOT SHARE” group). Upon running a difference of means test, what can Mr. Smith conclude about his hypothesis?

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t-Test: Two-Sample Assuming Equal Variances SHARE NOT SHARE Mean 8.636 10.26266667 Variance 4.425578378 8.457506306 Observations 75 75 Pooled Variance 6.441542342 Hypothesized Mean Difference df 148 t Stat -3.924815701 P(T<=t) one-tail t Critical one-tail 0.000066276675 1.655214506 P(T<=t) two-tail 0.000132553351 t Critical two-tail 1.976122494 t-Test: Two-Sample Assuming Equal Variances SHARE NOT SHARE Mean 8.636 10.26266667 Variance 4.425578378 8.457506306 Observations 75 75 Pooled Variance 6.441542342 Hypothesized Mean Difference df 148 t Stat -3.924815701 P(T<=t) one-tail t Critical one-tail 0.000066276675 1.655214506 P(T<=t) two-tail 0.000132553351 t Critical two-tail 1.976122494

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