Free response · Unit 3 Beta

Summer jobs: a two-proportion interval and the claims it supports

Q3: Inference (a test or an interval) · calculator allowed · 10 points

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The question

Name: ______________________   Date: ____________   Summer jobs: a two-proportion interval and the claims it supports (10 points)

Table

Summer jobs for juniors and seniors

A large school district wants to compare its juniors and seniors. It selects a random sample of 220 seniors and, separately, a random sample of 250 juniors, and asks each student whether they already have a summer job lined up. (Invented data.)
Students with a summer job lined up
GroupHave a job lined upSample size
Seniors121220
Juniors105250

  1. (a) Identify an appropriate inference procedure for estimating the difference between the proportion of all seniors and the proportion of all juniors in the district who have a summer job lined up, define the parameter, and verify the conditions for the procedure. [3 points]

  2. (b) Construct a 95% confidence interval for the difference. Show the expression with the values substituted. [2 points]

  3. (c) Interpret the interval in context. [2 points]

  4. (d) A counselor makes two claims: (i) seniors in the district are more likely than juniors to have a summer job lined up; (ii) the proportion of seniors with a job lined up is 25 percentage points higher than the proportion of juniors. Justify whether the interval supports each claim. [2 points]

  5. (e) Explain what the phrase "95% confidence" means in this context. [1 point]