A survey of nonprofit organizations showed that online fundraising increased in
ID: 3241052 • Letter: A
Question
A survey of nonprofit organizations showed that online fundraising increased in the past year. Based on a random sample of 54 nonprofit organizations, the mean one-time gift donation in the past year was $80, with a standard deviation of $12. 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. a. State the null and alternative hypotheses. Choose the correct answer below. A. H_0: mu lessthanorequalto 75 H_1: notequalto 75 B. H_0: mu = 80 H_1: notequalto 80 C. H0: mu = 80 H_1: mu > 80 D. H_0: notequalto 75 H_1: mu lessthanorequalto 75 E. H_0: mu lessthanorequalto 75 H_1: p > 75 F. H_0: mu lessthanorequalto 75 H_1: mu = 80 Find the test statistic. t_STAT = (Round to two decimal places as needed.) Find the p-value for this hypothesis test. p-value = (Round to three decimal places as needed.) What is the conclusion for this test? A. Reject the null hypothesis. There is sufficient evidence that the mean one-time gift donation is greater than $75. B. Do not reject the null hypothesis. There is insufficient evidence that the mean one-time gift donation is greater than $75. C. Reject the null hypothesis. There is insufficient evidence that the mean one-time gift donation is greater than $75. D. Do not reject the null hypothesis. There is sufficient evidence that the mean one-time gift donation is greater than $75. b. Interpret the meaning of the p-value in this problem. Choose the correct answer below. A. The p-value is the probability that the population mean one-time gift donation is $75 given that the sample mean one-time gift donation is $80. B. The p-value is the probability of getting a sample mean one-time gift donation of $80 or more, given that the population mean one-time gift donation is $75. C. The p-value is the probability that the population mean one-time gift donation is more than $75. D. The p-value is the probability that the population mean one-time gift donation is $80 or more.Explanation / Answer
a.State the null and alternative hypethesis. Choose the correct answer below.
Answer:
One wants to test if there is any evidence that the mean one-time gift donation is greater than $75.
Thus the correct answer is E. i.e
E. H0:75 Vs H1:>75
Find the test statistic.
n=54(sample size)
observed mean=80
observed std. dev.=12
true value=75
test statistic=(80-75)/(12/sqrt(54))=3.06 #sqrt: square root
Use the R-command below to get the p-vlaue:
pnorm(3.06,0,1,lower.tail=FALSE)
The p-value is 0.001106685 i.e. 0.001.
What is the conclusion for this test?
As p-value is smaller tahn 0.05, we reject H0 at 5% level of significance(los).
A. Reject the null hypothesis. There is sufficient evidence that the mean one-time gift donation is greater than $75.(at 5% los)
Interpret the meaning of p-value in this problem. Choose the correct answer below.
Here suppose sample mean (Xbar) follows a normal distribution with mean 75 and standard deviation 12/sqrt(54). Then then the probability that (Xbar) is greater than 80 is same as the p-value obtained above.
Hence the correct answer is:
B. The p-value is the probability of getting a sample mean one-time gift donation of $80 or more, given that the population mean one-time gift donation is $75.
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