Question:
Two random samples were taken to determine how often people in a community listen to the local radio station each month.
The first sample surveyed 15 people as they exited the bank on Main Street. The first sample found that the mean number of hours they listened to the radio each month was 20.
The second sample surveyed every sixth person as they exited the only local grocery store until 100 people were surveyed. The second sample found that the mean number of hours they listened to the radio each month was 12.
Which statements are true? Check all that apply.
A) The second sample is random.
B) The second sample is likely to be more representative of the population.
C) The first sample is likely to be more representative of the population.
D) The second sample will give a better representation because is it larger.
E) The first sample will give a better representation because it is smaller.
F) Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month.
Answer:
Options A, B, D, and F
Step-by-step explanation:
A) The second sample is random because in the second sample, people were surveyed at random. Every sixth person that exited the grocery store was surveyed and this selection represents an unbiased sampling method of the general population.
B) The second sample is likely to be more representative of the population, this is because, the sampling method was unbiased and it also contains a larger sample size than first sample.
D) The second sample will give a better representation because is it larger. Sample size is an important factor in a research. A large sample size gives a more accurate mean value than a small sample size.
F) Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month. This is because the research with the larger sample size is accepted instead of that of the smaller sample size. Also the second sample is likely to be more representative of the general population.
Options C and E are incorrect.
Thus, we can say that options A, B, D & F are correct.
