Question

A survey of nonprofit organizations showed that online fundraising has increased in the past year. Based on a random sample of 50 nonprofit organizations, the mean one-time gift donation in the past year was $62, with a standard deviation of $9. Test whether there is evidence that the mean one-time gift donation is different than $60?

Answer 1

Answer:

Check the explanation below.

Step-by-step explanation:

Hello!

The study variable is X: one-time online fundraising that a nonprofit organization has received.

Sample:

n= 50

sample mean X[bar]= $62

Standard deviation S= $9

You are interested in testing the average one-time donation is different than $60. Symbolically: μ ≠ 60

The hypothesis is:

H₀: μ = 60

H₁: μ ≠ 60

You didn't stat any significance level, I'll use a level of 5%

The critical region and the p-value for this test are two-tailed. Since all the available information is from the sample, assuming that the variable has normal distribution I've chosen the Student-t statistic:

t= X[bar] - μ ~ t$_{n-1}$

         S/√n

t= 62 - 60  = 1.57

    9/√50

The p-value for t=1.57 is 0.1228

Since the p-value: 0.1228 is greater than the significance level of 5%, the decision is to reject the null hypothesis. This means that the average one-time gift online fundraising that a nonprofit organization received is equal to $60.

I hope it helps!