Question

A survey was conducted of two types of marketers. The first type being marketers that focus primarily on attracting business​ (B2B), and the second type being marketers that primarily target consumers​ (B2C). It was reported that

523523

​(9090​%)

of B2B and

231231

​(5555​%)

of B2C marketers commonly use a business social media tool. The study also revealed that

310310

​(5353​%)

of B2B marketers and

245245

​(5858​%)

of B2C marketers commonly use a video social media tool. Suppose the survey was based on

582582

B2B marketers and

420420

B2C marketers. Complete parts​ (a) through​ (c) below.

a. At the 0.05 level of​ significance, is there evidence of a difference between B2B marketers and B2C marketers in the proportion that commonly use the business social media​ tool? Let population 1 correspond to B2B marketers and population 2 correspond to B2C marketers. Choose the correct null and alternative hypotheses below.

A.

Upper H 0H0​:

pi 1π1greater than or equals≥pi 2π2

Upper H 1H1​:

pi 1π1less than<pi 2π2

B.

Upper H 0H0​:

pi 1π1not equals≠pi 2π2

Upper H 1H1​:

pi 1π1equals=pi 2π2

C.

Upper H 0H0​:

pi 1π1less than or equals≤pi 2π2

Upper H 1H1​:

pi 1π1greater than>pi 2π2

D.

Upper H 0H0​:

pi 1π1equals=pi 2π2

Upper H 1H1​:

pi 1π1not equals≠pi 2π2

Your answer is correct.

Determine the test​ statistic,

Upper Z Subscript STATZSTAT.

Upper Z Subscript STATZSTATequals=

​(Type an integer or a decimal. Round to two decimal places as​ needed.)

Find the rejection region. Select the correct choice below and fill in the answer​ box(es) to complete your choice.

​(Round to three decimal places as​ needed.)

A.

ZSTATless than<minus−nothing

B.

ZSTATless than<minus−

or

ZSTATgreater than>plus+

Your answer is correct.

C.

ZSTATgreater than>plus+nothing

Determine a conclusion.

______

the null hypothesis. There

______

of a difference between B2B marketers and B2C marketers in the proportion of the business social media tool.

b. Find the​ p-value in​ (a) and interpret its meaning.

​p-valueequals=

​(Type an integer or a decimal. Round to three decimal places as​ needed.)

Interpret the​ p-value.

If the proportion of B2B marketers that use the business social media tool

is equal to

the proportion of B2C marketers that use the business social media​ tool, the probability that a

Upper Z Subscript STATZSTAT

test statistic

is less than

the one calculated is approximately equal to the​ p-value.

c. At the 0.05 level of​ significance, is there evidence of a difference between B2B marketers and B2C marketers in the proportion that use the video social media​ tool?

Let population 1 correspond to B2B marketers and population 2 correspond to B2C marketers. Determine the test​ statistic,

Upper Z Subscript STATZSTAT.

Upper Z Subscript STATZSTATequals=negative

Determine the​ p-value.

​p-valueequals=

​(Type an integer or a decimal. Round to three decimal places as​ needed.)

Determine a conclusion.

_______

the null hypothesis. There

__________

of a difference between B2B marketers and B2C marketers in the proportion of the video social media tool.

Answer 1

a. At the 0.05 level of significance, is there evidence of a difference between B2B marketers and B2C marketers in the proportion that commonly use the business social media tool? Let population 1 correspond to B2B marketers and population 2 correspond to B2C marketers.

The correct option is D.

D.

  

Determine the test statistic,

Where:

Find the rejection region.

Answer: B. or

Determine the conclusion: Reject the null hypothesis. There is evidence of a difference between B2B marketers and B2C marketers in the proportion of the business social media tool.

B) Find the p-value in (a) and interpret its meaning.

Answer:

Interpret the p-value.

If the proportion of B2B marketers that use the business social media tool is equal to the proportion of B2C marketers that use the business social media tool, the probability that a Zstat test statistic is less than or is greater than the one calculated is approximately equal to the p-value.

Part c.

Determine the test statistic,

Where:

p-value= 0.0582

Determine a conclusion.

Do not Reject the null hypothesis. There is no evidence of a difference between B2B marketers and B2C marketers in the proportion of the video social media tool.

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