Question

a consumer research 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 they like the food. 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 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 of the results are valid because the margin of error accounts for the differences in the results. c. both sample sizes are not adequate because less than one percent of the entire population is being surveyed. d. both of the results are not valid because the numbers are not the same. e. one of the results is not valid because it is not representative of the population being studied.

Explanation:

• Option A: Sample adequacy isn't just about sample size; representativeness matters. The second survey is only in the southern US, so A is wrong.
• Option B: The margin of error accounts for sampling variability. Both samples, if properly conducted (even with different scopes), can have valid results with margin of error explaining differences, so B is correct.
• Option C: Sample size adequacy isn't about percentage of population but representativeness and statistical power. So C is wrong.
• Option D: Different results don't mean invalid; samples can differ, so D is wrong.
• Option E: The second survey samples only the southern US to study all US people, so it's not representative. Thus, one result (from the southern - only survey) is not valid, so E is correct.

Answer:

B. Both of the results are valid because the margin of error accounts for the differences in the results.
E. One of the results is not valid because it is not representative of the population being studied.