A consulting firm gathers information on consumer preferences around the world to help companies monitor attitudes about​ health, food, and healthcare products. They asked people in many different cultures how they felt about the statement​ "I have a strong preference for regional or traditional products and dishes from where I come​ from." In a random sample of 810 ​respondents, 433 of 661 people who live in urban environments agreed​ (either completely or​ somewhat) with that​statement, compared to 75 out of 149 people who live in rural areas. Based on this​ sample, is there evidence that the percentage of people agreeing with the statement about regional preferences differs between all urban and rural​ dwellers?   Write the appropriate hypotheses to conduct a hypothesis test. Let p1 be the proportion of people living in urban environments that agree with the statement. Let p2 be the proportion of people living in rural environments that agree with the statement. Choose the correct answer below.     A. H0​: p1−p2=0 HA​: p1−p2>0   B. H0​: p1−p2=0 HA​: p1−p2≠0   C. H0​: p1−p2≠0 HA​: p1−p2=0   D. H0​: p1−p2>0 HA​: p1−p2=0   Determine the test statistic.   z=nothing ​(Round to two decimal places as​ needed.) Find the​ P-value.   P=nothing ​(Round to three decimal places as​ needed.) State the conclusion. Use a significance level of α=0.1. Choose the correct answer below.   ▼   Reject Do not reject the null hypothesis. There ▼   is is not sufficient evidence that the proportions of people that agree with the statement are different in urban and rural environments.

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A consulting firm gathers information on consumer preferences around the world to help companies monitor attitudes about​ health, food, and healthcare products. They asked people in many different cultures how they felt about the statement​ "I have a strong preference for regional or traditional products and dishes from where I come​ from." In a random sample of
810
​respondents,
433
of
661
people who live in urban environments agreed​ (either completely or​ somewhat) with that​statement, compared to
75
out of
149
people who live in rural areas. Based on this​ sample, is there evidence that the percentage of people agreeing with the statement about regional preferences differs between all urban and rural​ dwellers?
 
Write the appropriate hypotheses to conduct a hypothesis test. Let
p1
be the proportion of people living in urban environments that agree with the statement. Let
p2
be the proportion of people living in rural environments that agree with the statement. Choose the correct answer below.
 
 
A.
H0​:
p1−p2=0
HA​:
p1−p2>0
 
B.
H0​:
p1−p2=0
HA​:
p1−p2≠0
 
C.
H0​:
p1−p2≠0
HA​:
p1−p2=0
 
D.
H0​:
p1−p2>0
HA​:
p1−p2=0
 
Determine the test statistic.
 
z=nothing
​(Round to two decimal places as​ needed.)
Find the​ P-value.
 
P=nothing
​(Round to three decimal places as​ needed.)
State the conclusion. Use a significance level of
α=0.1.
Choose the correct answer below.
 
 
Reject
Do not reject
the null hypothesis. There
 
is
is not
sufficient evidence that the proportions of people that agree with the statement are different in urban and rural environments.
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