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StatisticsQ&A LibraryA survey of nonprofit organizations showed that online fundraising has increased in the past year. Based on a random sample of 55 nonprofit organizations, the mean one- time gift donation in the past year was $ 75, with a standard deviation of $ 9.If you test the null hypothesis at the 0.01 level of significance, is there evidence that the mean one- time gift donation is greater than $ 70?Interpret the meaning of the p- value in this problem.Question

Asked Nov 17, 2019

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A survey of nonprofit organizations showed that online fundraising has increased in the past year. Based on a random sample of 55 nonprofit organizations, the mean one- time gift donation in the past year was $ 75, with a standard deviation of $ 9.

- If you test the null hypothesis at the 0.01 level of significance, is there evidence that the mean one- time gift donation is greater than $ 70?
- Interpret the meaning of the p- value in this problem.

Step 1

**Hypotheses:**

*Null hypothesis:*

*H*_{0}: *µ* =70

*Alternative hypothesis:*

*H*_{1}: *µ* > 70

Since the alternative hypothesis states µ > 70, this test is a right-tailed test.

*Test statistic for t-test:*

Since population standard deviation is unknown, the appropriate test is one sample *t-*test.

**Decision rule:**

If p-value ≤ α, then reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Step 2

Here, the sample mean, *x*-bar is 75.

Sample standard deviation, *s* = 9

Sample size, *n* is 55.

The test statistic for *t*-test is calculated as **4.12** from the calculations given below.

Step 3

*Computation of P-value:*

The right tailed *P*-value for the *t*-test is 0.00007 which can be obtained using the excel formula,** “**=T.DIST.RT(4.12,54)”.

**Conclusion:**

Here, p-value (0.00007) is less than the signifi...

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