A small town is electing a new town council member. They decide to poll three random samples of registered voters to get an idea of which of the three candidates is most likely to be elected. Voters are asked to indicate the candidate they would vote for, if the election were tomorrow. Voters are also given the option of selecting "Undecided". The results of the poll are recorded in the table below.

Sample #1 Sample #2 Sample #3
Candidate #1 11 20 11
Candidate #2 27 23 28
Candidate #3 11 3 9
Undecided 1 4 2
Which candidate do you think will be elected?
How confident are you in your prediction? Explain your reasoning using complete sentences.

Mr. Wilson is giving his students a vocabulary test tomorrow over all the terms they have learned from this semester. Today, he wants to determine how prepared the students are for the test. So, he writes each term on a note card and puts all the note cards in a paper bag. Then, he asks each student to come to his desk, select five note cards out of the bag, define those five terms, and then put the note cards back in the bag. He records the number of terms each student is correctly able to define.

What is the population in this situation? What is the sample? Use complete sentences in your answer.
Do you think the data from the sample Mr. Wilson is collecting is representative of the population? Explain your reasoning using complete sentences.

A research group is on a college campus and is conducting a survey regarding the coffee consumption of college students in America. They randomly select three sample groups of 100 registered students to complete their survey, which asks the students to identify the average number of 8-ounce cups of coffee they consume each day. The results of the three sample groups are shown in the table below.

0 1 2 3 4+
Sample #1 38 19 26 16 1
Sample #2 32 14 37 15 2
Sample #3 41 22 31 6 0
One researcher looked at the results and made the following inference: "More college students don't drink coffee than do." Is this a valid conclusion? Explain your reasoning using complete sentences.

Jobs and productivity! how do retail stores rate? one way to answer this question is to examine annual profits per employee. the following data give annual profits per employee (in units of 1 thousand dollars per employee) for companies in retail sales. assume σ ≈ 4.0 thousand dollars. 3.7 6.7 3.6 8.5 7.5 5.9 8.7 6.4 2.6 2.9 8.1 −1.9 11.9 8.2 6.4 4.7 5.5 4.8 3.0 4.3 −6.0 1.5 2.9 4.8 −1.7 9.4 5.5 5.8 4.7 6.2 15.0 4.1 3.7 5.1 4.2 (a) use a calculator or appropriate computer software to find x for the preceding data. (round your answer to two decimal places.) thousand dollars per employee (b) let us say that the preceding data are representative of the entire sector of retail sales companies. find an 80% confidence interval for μ, the average annual profit per employee for retail sales. (round your answers to two decimal places.) lower limit -- thousand dollars upper limit -- thousand dollars (c) let us say that you are the manager of a retail store with a large number of employees. suppose the annual profits are less than 3 thousand dollars per employee. do you think this might be low compared with other retail stores? explain by referring to the confidence interval you computed in part (b). yes. this confidence interval suggests that the profits per employee are less than those of other retail stores. no. this confidence interval suggests that the profits per employee do not differ from those of other retail stores. correct: your answer is correct. (d) suppose the annual profits are more than 6.5 thousand dollars per employee. as store manager, would you feel somewhat better? explain by referring to the confidence interval you computed in part (b). yes. this confidence interval suggests that the profits per employee are greater than those of other retail stores. no. this confidence interval suggests that the profits per employee do not differ from those of other retail stores. (e) find an 95% confidence interval for μ, the average annual profit per employee for retail sales. (round your answers to two decimal places.) lower limit 3.75 incorrect: your answer is incorrect. thousand dollars upper limit 6.41 incorrect: your answer is incorrect. thousand dollars