Question

One of the most​ impressive, innovative advances in online fundraising over the past decade is the rise of​ crowd-funding websites. While features differ from site to​ site, crowd-funding sites are websites that allow you to set up an online fundraising campaign based around a fundraising​ page, and accept money directly from that page using the​ website's own credit card processor. A certain​ crowd-funding website reported that 127 of 347 technology​ crowd-funding projects were successfully launched in the past year and 347 of 882 film and video​ crowd-funding projects were successfully launched in the past year. Complete parts​ (a) through​ (c) below.
a. Is there evidence of a significant difference in the proportion of technology​ crowd-funding projects and film and video​ crowd-funding projects that were​ successful? (Use alpha ​= 0.1​.)
State the null and alternative​ hypotheses, where pi 1 is the population proportion of successful technology​ crowd-funding projects and pi 2 is the population proportion of successful film and video​ crowd-funding projects.

Answer 1

Data:    

n1 = 347   

n2 = 882   

p1 = 127/347 = 0.365994236   

p2 = 347/882 = 0.393424036   

Hypotheses:    

Ho: p1 = p2    

Ha: p1 ≠ p2    

Decision Rule:    

α = 0.1   

Lower Critical z- score =   -1.644853627

Upper Critical z- score = 1.644853627

Reject Ho if |z| >   1.644853627

Test Statistic:    

Average proportion, p = (n1p1 + n2p2)/(n1 + n2) = (347 * 0.365994236311239 + 882 * 0.393424036281179)/(347 + 882) = 0.385679414

q = 1 - p = 1 - 0.385679414157852 = 0.614320586

SE = √[pq * {(1/n1) + (1/n2)}] = √(0.385679414157852 * 0.614320585842148 * ((1/347) + (1/882))) = 0.030845206

z = (p1 - p2)/SE = (0.365994236311239 - 0.393424036281179)/0.030845206015453 = -0.889272711

p- value = 0.373856534   

Decision (in terms of the hypotheses):    

Since 0.889272711 < 1.644853627 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence of a significant difference in the proportion of technology​ crowd-funding projects and film and video​ crowd-funding projects that were​ successful.

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