STAtistics / Mr. Hansen 4/15/2009

Name: _________________________ Battery bonus (Mr. Hansen’s use only): __________

Cumulative Test Through Chapter 14

• Illegible or cryptic explanations may not earn full credit, even if your answers are numerically correct. In particular, the letter z must always be crossed, and the letter s must have a serif or two.
• Decimal approximations should always include at least 3 significant digits.
• Do not mark on your formula sheets. These are to be reused all year.
• If you happen to have spare batteries, leave them in plain view for a 1-point bonus.

Part I: Always, Sometimes, Never (3 pts. each)

In each blank, write A if the statement is always true, S if it is sometimes true, or N if it is never true. There is no partial credit.

___1.	In a LSRL t-test, the t statistic equals the computed slope, b1, divided by .
___2.	In a LSRL for which r = –0.998, the linear fit is valid.
___3.	The LSRL slope tells us the change in the response variable that the model predicts for each additional unit of the explanatory variable.
___4.	In a test for independence between two categorical variables, one of which has 13 categories and the other of which has 11 categories, the degrees of freedom for the test will equal 120.
___5.	If the 95% confidence interval for LSRL slope is , then there is good evidence at the level of a linear correlation between the explanatory and response variables.
___6.	A two-tailed two-proportion z test produces the same P-value as a 2-way test in a test for independence between two categorical variables. (Note: Assume each categorical variable is split into two exhaustive and mutually exclusive categories, such as male/non-male or yes/no.)
___7.	When we compute a LSRL for a bivariate data set, the standard deviation of the residuals changes dramatically as the explanatory variable changes.

Part II: Definitions and Fill-Ins (6 pts. each).

8.	independence (of categorical variables) is defined as follows [give definition in terms of marginal and conditional probabilities in order to earn full credit]:
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9.	P(Type I error) is defined as follows [give definition as a conditional probability in order to earn full credit]: __________________________________________
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10.	degrees of freedom for a goodness-of-fit test equals ____________________
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11.	degrees of freedom for a LSRL t-test equals _____________________________
	where n denotes ___________________________________________________

Part III: Short Work (5 pts. each)

Show your work (3 pts.) and produce the desired answer (2 pts.) for each question.

	The following table for questions 12-15 shows some made-up data from a census of 90 doctors by specialty and length of service at a large hospital.
		Cardiology	Oncology	Other	Total
	< 2 years	19	12	18	49
	2 years	13	11	17	41
12.	Compute the conditional probability of an oncology specialty, given that a doctor has fewer than 2 years of service.
13.	Compute the marginal probability of an oncology specialty.
14.	In a test for independence of specialty and length of service, compute the expected number of cardiologists with 2 or more years of service.
15.	The largest contribution to the statistic comes from the cell in the lower left corner of the table. Show the computation of this contribution only. (Do not show the computation of the entire statistic; show only the contribution that comes from the lower left corner cell.)

Part IV: Statistical Tests (20 pts. each)

Show all required steps, especially assumptions in which you identify the test by name. You are allowed to be rather brief in the computations that you show.

16.	Smokey has come under suspicion in Mr. Hansen’s F period geometry class. The students know that if Smokey were fair, then Doug’s brother Greg should be selected 1/19 of the time, “volunteer” should be selected 2/19 of the time, Mr. Hansen should be selected 1/19 of the time, and other students should be selected the rest of the time. The following are the results from 120 simulated random trials:
	Greg: 8
	volunteer: 9
	Mr. Hansen: 8
	other students: 95
(a)	Which of the four data items above shows the greatest relative departure from randomness? (Circle it.)
(b)	Is there overall evidence of a lack of randomness by Smokey? Perform a suitable test, continuing on reverse side if necessary.

17.	Here are some realistic (though fabricated) data on height versus shoe size for 15 male subjects. We will perform linear regression using height as the explanatory variable.
		Height (in.)	Shoe Size
		66	10
		67	9.5
		68	10
		69	10
		69.5	12
		70	11
		70.5	11.5
		71	11
		71	13
		72	14
		72	13.5
		72	13
		73	13.5
		75	14
		76	14
(a)	Compute the standard deviation (standard error) of the slope. Give proper notation for it, in addition to your numeric answer.
(b)	Compute a 90% confidence interval for the slope. Show a little bit of work.
(c)	Show all required steps and prove that there is good evidence that the true slope is positive. You do not need to show work in this portion. Use reverse side if necessary.