Aim for FiveStatistics

Question 1: Formulating questions and collecting data

A salad bar survey

  • Units 1 and 3
  • 10 points
  • About 22 minutes

You can use a calculator on this question, just like on exam day.

A multi-part question about a study's design: you identify sampling methods or study types, explain whether results can be generalized or show cause and effect, describe or choose a display, and write a valid investigative question. It focuses on Practices 1 and 2. On the exam: Question 1 of 4 (official name: Multi-Focus on Practices 1 and 2). Section II has 4 free-response questions in 90 minutes (50% of the score); each question is worth 10 points and 12.5% of the score. The exam is fully digital in Bluebook, a graphing calculator with statistical capabilities is expected, and the formula sheet and tables are provided.

The question and its sources

Show the work that leads to each answer, and explain your reasoning in the context of the situation. A graphing calculator with statistical capabilities, the formula sheet and the statistical tables are available. Use the information given to answer parts A through E, and label any subparts (for example, i and ii).

The salad bar decision

The student council at a high school with 1,800 students will ask the cafeteria to add a salad bar only if there is convincing evidence that more than 60% of students would buy lunch from it at least once a week.

The council has an alphabetical list of all 1,800 students. It plans to choose a random whole number from 1 to 15, select the student in that position on the list, and then select every 15th student after that, for a sample of 120 students. Each selected student will be asked whether they would buy lunch from a salad bar at least once a week.

Source: Hypothetical scenario

Suggested time: 22 minutes

Your answers are saved in this browser as you type.

Something wrong with this question?

What's wrong?

Please don't include personal details.

Part (A)

2 points

(i) Identify the sampling method the council plans to use. (ii) A council member suggests instead asking the first 120 students in the cafeteria lunch line on Monday. Explain how this method could lead to a biased estimate of the proportion of all students who would buy lunch from the salad bar at least once a week.

0 / 2,500 characters

Part (B)

1 point

The council emails the survey to the 120 selected students, and only 64 respond. Explain how this could bias the results.

0 / 2,500 characters

Part (C)

3 points

Suppose all 120 selected students respond. The council will test whether more than 60% of all students would buy lunch from the salad bar at least once a week. (i) Define the parameter of interest in context. (ii) State the null and alternative hypotheses. (iii) Identify the appropriate inference procedure.

0 / 2,500 characters

Part (D)

2 points

(i) Show that the 10% condition is met for this test. (ii) Show that the normality condition is met for this test.

0 / 2,500 characters

Part (E)

2 points

(i) Describe a Type I error in context, and describe one consequence of making it. (ii) Identify one change the council could make to its study that would increase the power of the test, and explain why.

0 / 2,500 characters

Checking scoring…

Scoring it yourself shows you the rubric, examples and a model answer. Try writing your answer first.