STAtistics / Mr. Hansen 4/12/2011

Name: _________________________

Sample Questions for Test on 4/14/2011

Instructions: For this test, you need to be thoroughly familiar with the Must-Pass Quiz, which we have been studying for more than 2 months (since Feb. 3), as well as all 7 pages of the AP formula sheet. There is a reasonable facsimile of the AP formula sheet, correct in all but pagination, near the back of your Barron’s AP review book. You are also expected to know the handout that clarifies the third page of the formula sheet. Since many of the questions will be straight from the MPQ or formula sheet, there is no point in repeating them here. Please refer to your MPQ and formula sheet notes when studying for those questions. Some harder “hybrid” questions, e.g., questions that require knowledge of something from the Must-Pass Quiz followed by application of a formula from the AP formula sheet, are also possible. NOTE: MOST OF THE QUESTIONS WILL NOT BE THIS HARD. The purpose of this handout is merely to show some questions of this type so that you are not surprised on Thurday. We did some other “hybrid” questions in class on Tuesday, 4/12. No solution key is provided. Answers are given below, with no explanations. However, if anyone would like to e-mail one or more proposed explanations to the sample questions below, Mr. Hansen will read and edit the responses and then post them on the class website as a public service. However, you have to put forth some effort. No solutions will be posted unless somebody tries to solve the problems.
1.	A 1-prop. z test has a null hypothesis that p = 0.39. In 800 trials, there are 300 successes.
(a)	List the assumptions you must check.
(b)	Compute the s.e.
(c)	Compute the test statistic.
(d)	Compute the 2-tailed P-value.
(e)	Write a believable conclusion, in some made-up context.
2.	In #1, compute the 2-tailed P-value if the s.e. is cut almost in half, to 0.01.
3.	Explain why the correct formula to use for the s.e. of the difference of proportions for a 2-prop. z test is usually not #5 on p. 3 of the AP formula sheet.
4.	For the following collection of (x, y) ordered pairs, compute the standard error of the LSRL slope: {(1.1, 4.8), (2.3, 5.1), (3.7, 6), (4.2, 6.9)}.
5.	If V and W are independent events, each having probability 0.3, compute the probability that at least one of them occurs.
6.	Let X and Y be mutually exclusive events, each having probability 0.4. Explain why X and Y cannot be independent.
7.	A fair die has a uniform distribution for the outcomes {1, 2, 3, 4, 5, 6}. Compute the variance and s.d. of the value of a die roll.
8.	A fair coin is flipped 432 times. Compute the probability of obtaining exactly 216 heads.
	ANSWERS
1.	(a) SRS,
	(b)
	(c) z = −0.8698
	(d) P = 0.3844
	(e) There is no evidence ( z = −0.8698, P > 0.3) that the proportion of seniors who are supercilious is different from 0.39.
2.	P = 0.1336
3.	Most of the time, in a 2-prop. z test, our null hypothesis is that p1 = p2. Therefore, the sampling distribution of must be constructed with s.e. given by formula #6, not #5.
4.
5.
6.	(Proof by contradiction.) If X and Y were independent, then by the alternate definition of independence. That contradicts the known fact that since X and Y were given to be mutually exclusive. (Q.E.D.)
7.	Let X = random vbl. denoting die outcome. Var(X) = 2.9167
8.	P(216 heads) = 0.0384