Political Contributions: Listed below are contributions (in dollars) made to the two presidential candidates in a recent election. All contributions are from the same zip code as the author, and the data are from the Huffington Post. Do the contributions appear to favor either candidate? What do you conclude after learning that there were 66 contributions to Obama and 20 contributions to McCain.
McCain:
50
75
240
305
250
700
350
500
1250
1500
500
500
40
221
400
Obama:
275
452
300
1000
1000
500
100
1061
1200
235
875
2000
350
210
250
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Does it exceed your level of significance?
Going only with the number of contributions favors Obama.
To determine if the contributions favor either candidate, we can calculate the average contribution for each candidate and compare them.
To calculate the average contribution for each candidate, we need to add up all the contributions made to each candidate and divide it by the total number of contributions.
For McCain:
Total contributions to McCain = 50 + 75 + 240 + 305 + 250 + 700 + 350 + 500 + 1250 + 1500 + 500 + 500 + 40 + 221 + 400 = 6416
Total number of contributions to McCain = 15
Average contribution to McCain = Total contributions to McCain / Total number of contributions to McCain = 6416 / 15 ≈ 427.73
For Obama:
Total contributions to Obama = 275 + 452 + 300 + 1000 + 1000 + 500 + 100 + 1061 + 1200 + 235 + 875 + 2000 + 350 + 210 + 250 = 9053
Total number of contributions to Obama = 15
Average contribution to Obama = Total contributions to Obama / Total number of contributions to Obama = 9053 / 15 ≈ 603.53
From the calculations, we can see that the average contribution for Obama ($603.53) is higher than the average contribution for McCain ($427.73). Therefore, it appears that the contributions favor Obama in this case.
However, it's also worth noting that the number of contributions does not necessarily indicate the overall favorability. In this case, there were 66 contributions to Obama and 20 contributions to McCain. So, even though the average contribution favors Obama, it's important to consider the individual contribution amounts and the proportion of contributions to each candidate.