Question

A survey of non–profit organizations showed that fundraising has increased past year. Based on a sample of 30 non–profit organizations the mean one–time gift donation in the past year was $75 with standard deviation of $9. At the 0.01 level of significance, is there evidence that the mean one–time gift donation is greater than $70.

Answer 1

Solution :

Given

sample mean = 75 and standard error of sample mean = = 9/square root(30) = 1.643

Let the actual mean be mu.

a) Probability ( mu > 70) = Probability ((mu-sample mean)/sigma mean > (70 - 75)/1.643)

We know that (mu-sample mean)/sigma mean is a standard normal variable. So, we have to use normal distribution tables or excel's normsdist() function to find this probability.

P( Z > (70 - 75)/1.643 ) = P (Z> -3.04) = 1 - P (Z <-3.04) = 1 - N (-3.04) = 1 - 0.0011829 = 0.9988171 =0.9988 = 99.88 %

To say that there is evidence that mean one-time gift donation is greater than $70 with 0.01 level of significance, you will have to reject the null hypothesis that mean < 7. with a 99% probabilty. But there is only 99.88% probability with which you can say this is not valid. So, at 0.01 level significance, you cannot say there is enough evidence to say that the mean one-time gift-donation is greater than $70 .

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