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.

  1. 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?
  2. Interpret the meaning of the p- value in this problem.
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Expert Answer

Step 1

Hypotheses:

Null hypothesis:

H0: µ =70

Alternative hypothesis:

H1: 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.

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t = 75-70 55 =4.12

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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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