Question

1. In a sample of 625 airline travelers, 485 collected "airline miles" toward free trips. What does the number 140/625 represent?
The probability that a passenger collects airline miles
The sample proportion of the travelers who do not collect airline miles
The sample proportion of the travelers who collect airline miles
The margin of error for the sample
2.A random sample of people answered the question "Do you collect airline miles?" The margin of error for the sample was +-2%. The sample proportion of people who answered no was 3/10. How many people in the sample answered no?
15
225
750
2500
3.A research group had a stack of survey responses. The number of respondents was more than 5000 and fewer than 5500. When the researchers divided the respondents into 13 equal groups, there were no extra respondents. Similarly, there were no extra respondents when they divided the responses into 7 equal groups or 11 equal groups. How many respondents were there?
1001
5005
5031
500,500
4. An event occurs 96 times in a sample of 900. Find its sample proportion and margin of error.
5. a. It costs $20 to interview each person for a survey. Find the cost to obtain a +-3% margin of error.

b. Find the cost to obtain a +-2% margin of error. Why do you think polls with smaller margins of error are rare?
6. a. A poll of 150 voters shows that a candidate is preferred by 56% of the voters while 44% prefer the opponent. Should the candidate be concerned? Explain.

b. A later poll of 600 voters shows the candidate is preferred by 55% of the voters. Should this candidate feel more or less confident, given the results of the second poll? Explain.

Answer 1

1. In a sample of 625 airline travelers, 485 collected "airline miles" toward free trips. What does the number 140/625 represent?

The sample proportion of the travelers who do not collect airline miles


3.A research group had a stack of survey responses. The number of respondents was more than 5000 and fewer than 5500. When the researchers divided the respondents into 13 equal groups, there were no extra respondents. Similarly, there were no extra respondents when they divided the responses into 7 equal groups or 11 equal groups. How many respondents were there?

5005

5005 / 13 = 385
5005 / 7 = 35,035
5005 / 11 = 455

6. a. A poll of 150 voters shows that a candidate is preferred by 56% of the voters while 44% prefer the opponent. Should the candidate be concerned? Explain. 

150 voters = 84 candidate ; 66 opponent

The candidate can be confident that for every 150 voters, 84 of them will vote for him. However, 150 is a small number compared to a population, thus, the candidate must continue his campaign to turn voters into his favor.

b. A later poll of 600 voters shows the candidate is preferred by 55% of the voters. Should this candidate feel more or less confident, given the results of the second poll? Explain.

600 x 55% = 330 voters are for the candidate. The candidate can feel more confident because the initial poll rating still holds true as the number of sample population increases.