After the 2010 earthquake in Haiti, many charitable organizations conducted fund

Question

After the 2010 earthquake in Haiti, many charitable organizations conducted fundraising campaigns to raise money for emergency relief. Some of these campaigns allowed people to donate by sending a text message using a cell phone to have the donated amount added to their cell-phone bill. The report "Early Signals on Mobile Philanthropy: Is Haiti the Tipping Point?" (Edge Research, 2010) describes the results of a national survey of 1526 people that investigated the ways in which people made donations to the Haiti relief effort.

The report states that 17% of Gen Y respondents (those born between 1980 and 1988) and 14% of Gen X respondents (those born between 1968 and 1979) said that they had made a donation to the Haiti relief effort via text message. The percentage making a donation via text message was much lower for older respondents. The report did not say how many respondents were in the Gen Y and Gen X samples, but for purposes of this exercise, suppose that both sample sizes were 400 and that it is reasonable to regard the samples as representative of the Gen Y and Gen X populations.

(a) Is there convincing evidence that the proportion of those in Gen Y who donated to Haiti relief via text message is greater than the proportion for Gen X? Use

= 0.01.

(Use a statistical computer package to calculate the P-value. Use Y X. Round your test statistic to two decimal places and your P-value to three decimal places.)

=

=

Explanation / Answer

Step 1 - State the hypothesis:

Null hypothesis: P1 <= P2
Alternative hypothesis: P1 > P2

The null hypothesis will be rejected if the proportion of Gen Y making donations vai text message (p1) is sufficiently greater than the proportion of Gen X making donations vai text message(p2).

Step 2 - Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a two-proportion z-test.

Step 3 - Analyse sample data

We need to calculate the pooled sample proportion(p) and standard error. Using these measures, we compute the z-score test statistic.

p = (p1 * n1 + p2 * n2) / (n1 + n2) = (0.17 * 400 + 0.14 *400)/(400 + 400) = 0.155

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

= sqrt{ 0.155 * (1 - 0.155) * [ (1/400) + (1/400) ] }

= sqrt{ 0.130975 * 0.005} = sqrt(0.000654875) = 0.02559053

z = (p1 - p2) / SE = (0.17 - 0.14)/0.02559053 = 1.172309

Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 1.172309

p value = 1 - 0.87946 = 0.12054

Step 4 - Interpret the results

Since the P-value (0.12054) is greater than the significance level (0.01), we cannot reject the null hypothesis.

So there is no convincing evidence that the proportion of those in Gen Y who donated to Haiti relief via text message is greater than the proportion for Gen X

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