Question

A consulting firm asks people in many different cultures how they felt about the following​ statement: I try to avoid eating fast foods. In a random sample of 797 ​respondents, 412 people were 35 years old or​ younger, and, of​ those, 195 agreed​ (completely or​ somewhat) with the statement. Of the 385 people over 35 years​ old, 241 people agreed with the statement. Complete parts a and b below.

​a) Is there evidence that the percentage of people avoiding fast food is different in the two age​ groups?

State the null and alternative hypotheses. Choose the correct answer below.

A.

H0​: The proportion of respondents 35 years old or younger is greater than or equal to the proportion of respondents over 35 years old.

HA​: The proportion of respondents 35 years old or younger is less than the proportion of respondents over 35 years old.

B. H0​: The proportion of respondents 35 years old or younger is less than or equal to the proportion of respondents over 35 years old.

HA​: The proportion of respondents 35 years old or younger is greater than the proportion of respondents over 35 years old.

C. H0​: The proportions are different.

HA​: The proportions are the same.

D. H0​: The proportions are the same.

HA​: The proportions are different.

Determine the chi squaredχ2 statistic.

x2=____

Find the​ P-value.

p=____

Is there evidence that the percentage of people avoiding fast food is different in the two age​ groups?

b) Give a 99​% confidence interval for the difference p1−p2​, where p1 and p2 are the proportions of respondents 35 years old or younger and respondents over 35 years​ old, respectively.

The 99​% confidence interval is:

(____,  _____)

Answer 1