A survey of nonprofit organizations showed that online fundraising increased in

Question

A survey of nonprofit organizations showed that online fundraising increased in the past year. Based on a random sample of 60 nonprofit organizations, the mean one-time gift donation in the past year was $80, with a standard deviation of $10.

A: If you test the null hypothesis at the 0.05 level of significance, is there evidence that the mean one-time gift donation is greater than $75?

B: Interpret the meaning of the p-value in this problem.

Find the Test Stat:

Find the p- value:

Use the information given above to determine whether or not to reject the null hypothesis. If the null hypothesis is rejected, there is sufficient evidence that the mean one-time gift donation is greater than$75

Otherwise there is insufficient evidence that the mean one-time gift donation is greater than $75.

b. Interpret the meaning of the p-value in this problem.

Explanation / Answer

Below are the null and alternate hypothesis
H0: u <= 75
H1: u > 75

sample mean = 80, sample size n = 60 and std. dev. = 10

Test statistics,
t = (80-75)/(10/sqrt(60)) = 3.873

degrees of freedom = 60 - 1 = 59

p-value = 0.000136

As p-value is less than the significance level of 0.05, we reject the null hypothesis.
This means there is sufficient evidence that the mean one-time gift donation is greater than$75.

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