please show all steps including assumptions. After the 2017 hurricanes that hit
ID: 3044055 • Letter: P
Question
please show all steps including assumptions.
After the 2017 hurricanes that hit Texas and Florida, many charitable organizations conducted fundraising campaigns to raise money for emergency relief. A survey was conducted to investigate the ways in which people made donations to the hurricane relief efforts. 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 hurricane relief efforts via text message. A total of 400 Gen Y respondents and 400 Gen X respondents were randomly sampled. (2 points) Is there convincing evidence that the proportion of those in Gen Y who donated to hurricane relief via text message is greater than the proportion for Gen X? Use = 0.01. Please do this test by-hand using the Classical (Critical Value) Approach. a. b. (2 points) Estimate the difference between the proportion of Gen Y and Gen X that made a donation via text message using a 98% confidence interval. Does your interval support the conclusion you made in part (a)? (2 points) Do the test in part a again, this time using the SPSS software. Include the appropriate software output, and show the 6-steps of the testing process again (even though you've done them in part a). Use the p-value approach with the software. C.Explanation / Answer
a) H0: p1 = p2
H1: p1 > p2
The pooled sample proportion 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))
= 0.026
The test statistic z = (p1 - p1)/SE
= (0.17 - 0.14)/0.026
= 1.15
At alpha = 0.01, the critical value is z0.005 = 2.58
As the critical value is greater than the test statistic value(2.58 > 1.15), so the null hypothesis is not rejected.
so at alpha = 0.01 there is not sufficient evidence to support the claim thatA the proportion of those in Gen Y is greater than the proportion for Gen x.
b) At 98 % confidence interval the critical value is z0.01 = 2.33
The confidence interval is
(p1 - p2) +/- z0.01 * SE
= (0.17 - 0.14) +/- 2.33 * 0.026
= 0.03 +/- 0.06
= -0.03, 0.09
As the interval cointains the hypothised value 0, so the null hypothesis is not rejected.
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