A national food company surveyed 2,400 people throughout the United States to determine whether or not people in the United States enjoy a certain type of hot dog. Of those surveyed, 52% of the people said that they like the food.

Question

Another company surveyed 1,100 people throughout the southern part of the United States to determine whether or not people in the United States enjoy the same type of hot dog. Of those surveyed, 60% of the people said that they like the food.

Select two statements that must be correct about the surveys.
A.
Both sample sizes are adequate because 1,100 and 2,400 people were surveyed.

B.
Both sample sizes are not adequate because less than one percent of the entire population is being surveyed.

C.
Both of the results are valid because the margin of error accounts for the differences in the results.

D.
One of the results is not valid because it is not representative of the population being studied.

E.
Both of the results are not valid because the numbers are not the same.

Answer 1

The correct statements about the surveys are:

A. Both sample sizes are adequate because 1,100 and 2,400 people were surveyed.
(Due to the relatively large sample sizes, both samples can be considered adequate for drawing general conclusions about their respective populations.)

D. One of the results is not valid because it is not representative of the population being studied.
(The second survey is limited to the southern part of the United States, which may not be representative of the overall U.S. population. Thus, its findings may not be generalized to the entire country.)

The other options are not necessarily correct: B. Statements about adequacy cannot be made simply based on percentages of the population without full context. C. The validity of the results depends on how representative the samples are, not just on margins of error. E. Differences in numbers do not invalidate survey results; rather, their relevance to their respective populations matters.