John Smith, Director of the NJ Nonprofits Working Group, is interested in the em

Question

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?

t-Test: Two-Sample Assuming Equal Variances SHARE NOT SHARE 8.636 10.26266667 4.4255783788.457506306 75 Mean Variance Observations Pooled Variance Hvpothesized Mean Difference df t Stat P(T

Explanation / Answer

As we are trying to test the difference of means here in the two groups, therefore we look at the 2 tailed test here. The pvalue here is computed from the t distribution tables as:

p = 2P( tn1+n2-2 < -3.9248 )

Note that we could either find the above p-value from the t distribution tables or do the test using the critical t value for a two tailed test. Here we are given the critical two tail t value as 1.9761

Now as -1.9761 > -3.9248, therefore it lies in the rejection region and we can reject the null hypothesis here and conclude that we have sufficient evidence that there is a difference in means of the 2 groups.

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