A Flat Tire? I heard the following joke from my colleague. Four students failed to show up
Question:
A Flat Tire?
I heard the following joke from my colleague. Four students failed to show up in Final Exam. They claimed that they shared a car on a field trip one week before the exam and had a flat tire, thus could not get back in time. They asked for a make-up exam. The professor agreed. He put each of them in separate rooms and gave only two questions. One question is very easy and worth 5 points. The other question is worth 95 points: which tire is flat?
You are smart enough to get the joke: if the students all claim the same tire, professor will let them pass, otherwise they will be in trouble! I want you to think what professor does as a hypothesis testing. Let's say the four students are A, B, C and D. Their answers could be either of FL (front left), FR (front right), RL (rear left) or RR (rear right). A set of collected answers could be (FL, FL, FR, RR) (from (A, B, C, D), respectively).
PS: This question will require a little calculation. High school level would be sufficient. If you get all concepts and procedures correct, there will be no deduction of score for wrong calculation of numbers.
Which set of hypotheses represents professor's null and alternative hypotheses?
☐ H0: Students told the truth. Ha: Students invented an excuse.
☐ H0: Students invented an excuse. Ha: Students told the truth.
Sample statistic
Remember statistic is "a function of sample", i.e. sample mean, sample standard deviations, etc. You may phrase your answer as:
Answer: The sample statistic is defined as _____ (fill in a subclause). According to this definition, the set of answers (FL, FL, FL, FL) has the statistic value of __ (fill in a number), while (FR, FL, RR, FL) has the statistic value of __ (fill in a number).
Rejection Region (for the sample statistic)
Answer: Using the sample statistic defined in the previous sentence, the rejection region, intuitively, should be {_____} (fill in a number, or a collection of numbers).
Type-I-Error rate α of the Rejection Region defined in the previous question
Hint: Calculate a number and briefly show how you get this number.
Answer: α = P({Sample statistic in RR}| H0) = ____.
Having collected the four students' answers, how do you define the p-value of such answers for this test?
Answer: If I received the four students' answers as (FL, FL, FL, RR), the p-value will be
P(X > // ≥ // < // ≤ __) = ___.
If I received (FL, FL, FL, FL), the p-value will be
P(X > // ≥ // < // ≤ __) = ___.
Give professor a guideline, summarizing your results in previous questions.
Answer: Professor will believe that the students are lying // telling the truth, if their answers satisfy that ____ (fill in a subclause). This is a test with Type-I-Error rate ____ (fill in a number). According to this test, if the student turn in an answer of (__, __, __, __), he believes they are lying // telling the truth (p-value = __). If they turn in an answer of (__, __, __, __), he will not be able to reach a conclusion (p-value = __).
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill