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 344 technology​ crowd-funding projects were successfully launched in the past year and 355 of 890 film and video​ crowd-funding projects were successfully launched in the past year. Complete parts​ (a) through​ (c) below. Part 1 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 α= 0.01.) a. State the null and alternative​ hypotheses, where π1 is the population proportion of successful technology​ crowd-funding projects and π2 is the population proportion of successful film and video​ crowd-funding projects.   A. H0​:π1=π2H1​:π1≠π2 B. H0​:π1=π2H1​:π1<π2 C. H0​:π1≠π2H1​:π1<π2 D. H0​:π1≠π2H1​:π1>π2 E. H0​:π1≠π2H1​:π1=π2 F. H0​:π1=π2H1​:π1>π2   b.Determine the value of the test statistic. ​(Type an integer or a decimal. Round to two decimal places to the right of the decimal point as​ needed.) A.ZSTAT =(0.369 − 0.399)(0.391)•(1−0.391)•1344 + 890 = −0.030.000193 = −2.16​, using formulas​ (10.5) B.ZSTAT =(0.399 − 0.369)(0.391)•(1−0.391)•1344 + 1890 = 0.030.0009596 = +0.96​, using formulas​ (10.5) C.ZSTAT =(0.369 − 0.399)(0.391)•(1−0.391)•1344 + 1890 = −0.030.0009596 = −0.96​, using formulas​ (10.5) D.ZSTAT =(0.369 − 0.399)(0.391)• (0.391)•1344 + 1890 = −0.030.000616 = −1.29​, using formulas​ (10.5) c.Determine the critical​ value(s) for this test of hypothesis.​ Remember, for this​ question,α​= 0.01. ​(Round to two decimal places to the right of the decimal point as needed. Use a comma to separate answers as​ needed.)   A.​-2.58 , determined by​ NORM.S.INV(0.01/2) B.​-2.58, +2.58​ , determined by±​NORM.S.INV(0.01/2) C.​-0.01, +0.01​ , determined by±​NORM.S.INV(0.99/2) D.​-2.33, +2.33​ , determined by±​NORM.S.INV(0.01)   d.State the conclusion. ▼Do not reject/Reject the null hypothesis. There is▼sufficient/insufficient evidence to support the claim that there is a statistically significant difference in the proportion of successful technology​ crowd-funding projects and successful film and video​ crowd-funding projects.   e. Determine the​ p-value in​ (a) and interpret its meaning.The probability of obtaining a difference in proportions that gives rise to a test statistic▼greater than or equal tomore extreme or equal to less than or equal to contained in the interval between the▼negative test statistic test statistic test statistic and its negative is equal to the   A.​ p-value =​ 1-(NORM.S.DIST(-0.96,1)) = 0.831 B.​ p-value =​ (NORM.S.DIST(-0.96,1)) = 0.169 C. ​p-value =​ 2*(NORM.S.DIST(-0.96,1)) = 0.338 D. ​p-value =​ 2*(NORM.S.DIST(-0.96,0) = 0.504   if there is no difference between the population proportions of successful technology​ crowd-funding projects and successful film and video​ crowd-funding projects.   f. Construct and interpret a​ 99% confidence interval estimate for the difference between the proportion of technology​ crowd-funding projects and film and video​ crowd-funding projects that are successful. ​(Type integers or decimals. Round to four decimal places to the right of the decimal point as​ needed.)   A. 0.3884 ≤ π ≤ 0.3928 ​, from 0.3906 ±​CONFIDENCE.NORM(0.01,0.03,1234) B. −0.092 ≤ π ≤ 0.032 ​, found using formula​ (10.6): (0.3692 − 0.3989) ± 2.58 • 0.3692 • 0.3692344 + 0.3989 • 0.3989890 C. −0.1089 ≤ π ≤ 0.0496 ​, found using formula​ (10.6): (0.3692 − 0.3989) ± 2.58 • 0.3692 • (1 − 0.3692)344 + (0.3989 • (1 − 0.3989)890 D. 0.311 ≤ π ≤ 0.471 , found using formula​ (10.6): (0.3906) ± 2.58 • 0.3906 • 0.3906344 + 0.3906 • 0.3906890 The researchers performing this study can be​ 99% confident that the difference in the population proportion between successful technology​ crowd-funding projects and successful film and video​ crowd-funding projects is within the confidence interval stated above.

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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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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 344 technology​ crowd-funding projects were successfully launched in the past year and 355 of 890 film and video​ crowd-funding projects were successfully launched in the past year. Complete parts​ (a) through​ (c) below.
Part 1
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
α= 0.01.)
a. State the null and alternative​ hypotheses, where π1 is the population proportion of successful technology​ crowd-funding projects and π2 is the population proportion of successful film and video​ crowd-funding projects.
 
A. H0​:π1=π2H1​:π1≠π2
B. H0​:π1=π2H1​:π1<π2
C. H0​:π1≠π2H1​:π1<π2
D. H0​:π1≠π2H1​:π1>π2
E. H0​:π1≠π2H1​:π1=π2
F. H0​:π1=π2H1​:π1>π2
 
b.Determine the value of the test statistic. ​(Type an integer or a decimal. Round to two decimal places to the right of the decimal point as​ needed.)
A.ZSTAT =(0.369 − 0.399)(0.391)•(1−0.391)•1344 + 890 = −0.030.000193 = −2.16​, using formulas​ (10.5)
B.ZSTAT =(0.399 − 0.369)(0.391)•(1−0.391)•1344 + 1890 = 0.030.0009596 = +0.96​, using formulas​ (10.5)
C.ZSTAT =(0.369 − 0.399)(0.391)•(1−0.391)•1344 + 1890 = −0.030.0009596 = −0.96​, using formulas​ (10.5)
D.ZSTAT =(0.369 − 0.399)(0.391)• (0.391)•1344 + 1890 = −0.030.000616 = −1.29​, using formulas​ (10.5)

c.Determine the critical​ value(s) for this test of hypothesis.​ Remember, for this​ question,α​= 0.01. ​(Round to two decimal places to the right of the decimal point as needed. Use a comma to separate answers as​ needed.)
 
A.​-2.58 , determined by​ NORM.S.INV(0.01/2)
B.​-2.58, +2.58​ , determined by±​NORM.S.INV(0.01/2)
C.​-0.01, +0.01​ , determined by±​NORM.S.INV(0.99/2)
D.​-2.33, +2.33​ , determined by±​NORM.S.INV(0.01)
 
d.State the conclusion.
▼Do not reject/Reject the null hypothesis. There is▼sufficient/insufficient evidence to support the claim that there is a statistically significant difference in the proportion of successful technology​ crowd-funding projects and successful film and video​ crowd-funding projects.
 
e. Determine the​ p-value in​ (a) and interpret its meaning.The probability of obtaining a difference in proportions that gives rise to a test statistic▼greater than or equal tomore extreme or equal to less than or equal to contained in the interval between the▼negative test statistic test statistic test statistic and its negative is equal to the
 
A.​ p-value =​ 1-(NORM.S.DIST(-0.96,1)) = 0.831
B.​ p-value =​ (NORM.S.DIST(-0.96,1)) = 0.169
C. ​p-value =​ 2*(NORM.S.DIST(-0.96,1)) = 0.338
D. ​p-value =​ 2*(NORM.S.DIST(-0.96,0) = 0.504
 
if there is no difference between the population proportions of successful technology​ crowd-funding projects and successful film and video​ crowd-funding projects.
 
f. Construct and interpret a​ 99% confidence interval estimate for the difference between the proportion of technology​ crowd-funding projects and film and video​ crowd-funding projects that are successful. ​(Type integers or decimals. Round to four decimal places to the right of the decimal point as​ needed.)
 
A. 0.3884 ≤ π ≤ 0.3928 ​, from 0.3906 ±​CONFIDENCE.NORM(0.01,0.03,1234)
B. −0.092 ≤ π ≤ 0.032 ​, found using formula​ (10.6): (0.3692 − 0.3989) ± 2.58 • 0.3692 • 0.3692344 + 0.3989 • 0.3989890
C. −0.1089 ≤ π ≤ 0.0496 ​, found using formula​ (10.6): (0.3692 − 0.3989) ± 2.58 • 0.3692 • (1 − 0.3692)344 + (0.3989 • (1 − 0.3989)890
D. 0.311 ≤ π ≤ 0.471 , found using formula​ (10.6):
(0.3906) ± 2.58 • 0.3906 • 0.3906344 + 0.3906 • 0.3906890

The researchers performing this study can be​ 99% confident that the difference in the population proportion between successful technology​ crowd-funding projects and successful film and video​ crowd-funding projects is within the confidence interval stated above.
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