Question

Part 1: 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

α = 0.01.

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

z	=
P-value	=

Part 2:

(b) Estimate the difference between the proportion of Gen Y and the proportion of Gen X that made a donation via text message using a 99% confidence interval. (Round your answers to three decimal places.)

( ____ , ____ )

Answer 1

Solution:-

a)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P_Y< P_X  
Alternative hypothesis: P_Y > P_X

Note that these hypotheses constitute a one-tailed test.

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

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = (p₁ * n₁ + p₂ * n₂) / (n₁ + n₂)

p = 0.155

SE = sqrt{ p * ( 1 - p ) * [ (1/n₁) + (1/n₂) ] }
SE = 0.025591
z = (p₁ - p₂) / SE

z = 1.17

where p₁ is the sample proportion in sample 1, where p₂ is the sample proportion in sample 2, n₁ is the size of sample 1, and n₂ is the size of sample 2.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than -2.13

Thus, the P-value = 0.017.

Interpret results. Since the P-value (0.017) is greater than the significance level (0.01), we failed to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the proportion of those in Gen Y who donated to Haiti relief via text message is greater than the proportion for Gen X.

b) 99% confidence interval for the difference between the proportion of Gen Y and the proportion of Gen X is C.I = ( - 0.036, 0.096).

C.I = (0.17 - 0.14) + 2.576 × 0.025591

C.I = 0.03 + 0.0659224

C.I = ( - 0.0359, 0.0959)