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.

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 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.

Accepted Answer

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