A survey of nonprofit organizations showed that online fundraising increased in the past year. Based on a random sample of 53 nonprofit organizations, the mean one-time gift donation in the past year was $80,with a standard deviation of $13..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?a. State the null and alternative hypotheses. Choose the correct answer below.b. Find the test statistic. c. Find the p-value for this hypothesis test.

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Description: A survey of nonprofit organizations showed that online fundraising increased in the past year. Based on a random sample of 53 nonprofit organizations, the mean one-time gift donation in the past year was $80,with a standard deviation of $13..If y

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A survey of nonprofit organizations showed that online fundraising increased in the past year. Based on a random sample of 53 nonprofit organizations, the mean one-time gift donation in the past year was $80,
with a standard deviation of $13.

.	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?

a. State the null and alternative hypotheses. Choose the correct answer below.

b. Find the test statistic.

c. Find the p-value for this hypothesis test.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Let X be the random variable such that number of one-time gift donation

x̅: Sample mean of the number of one-time gift donation = 80

s: Sample standard deviation of the number of one-time gift donation = 13

n: Random sample size of the number of one-time gift donation = 53

It is asked to test whether at the 0.05 level of significance, is there evidence that the mean one-time gift donation is greater than $75.

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