AP Statistics / Mr. Hansen	Name: _______________________________________
4/19/2007

Test on Inferential Statistics

• Calculator is OK throughout.
• For questions 3 through 7, work is not expected. Simply write the type of test used, the df (write N/A if not applicable), the P-value, and the answer to the question posed.
• Throughout today’s test, we will use an a level of .02 to determine significance.
• Hint: For questions 6 and 7, some rounding may be required.
• Point values are shown in parentheses in the left margin. Your initials are worth 20 points.
• Initial here to indicate that you understand these instructions: ________

1. (20)

Do a full test (all steps, including the sketch) for the following problem. We are interested in knowing if the variables of hair color and bossiness are related or not at Borgetown Brep. In a census of 619 students, we observe the following data. Allow about 13 minutes for this problem.

	Not bossy	Moderately bossy	Very bossy
Red-haired	25	35	30
Brown-haired	72	70	69
Black-haired	60	50	48
Blonde	44	55	61

2.(a) (10)	Show that the cutoff value for determining significance or lack of significance in a 1-sample test for means is 4.286 if the hypothesized mean is 3, the alternative hypothesis is that m > 3, s = 2.2 from the data, and our sample size is 15 with no outliers or dramatic skewness.
(b) (10)	Draw a sketch to estimate the power of the test against the alternative hypothesis m = 4.
(c) (10)	Draw a sketch to show that the power would increase if all facts were as before, except with a sample size of 17.

3. (6)

Several STA freshmen test Gax Body Spray to see if it makes them more appealing to NCS students. Does it? Trials are performed double-blind, order randomized.

Subject #	Attractiveness Score (placebo)	Attractiveness Score (Gax)
1	15	18
2	14	11
3	14	15
4	12	10
5	20	20
6	8	7
7	6	7

Test used: ________________________ df = ________  P = ________
Answer: ___________________________________________________________________

4. (6)

Is this die unfair? We would expect proportions in the table to be 1/6, 1/3, 1/2.

Outcome	# of occurrences
“6”	17
other even values	38
odd values	66

Test used: ________________________ df = ________  P = ________
Answer: ___________________________________________________________________

5. (6)

I run a LSRL of men’s ages (X) versus surveyed minimum acceptable women’s ages to date (Y) with 25 data points. The residuals are normally distributed about the line and show no other patterns. If , do I have adequate evidence of a positive linear correlation between X and Y?

Test used: ________________________ df = ________  P = ________
Answer: ___________________________________________________________________

6. (6)

In my pre-election polling, Obama has 22% support (sample size of 520). Is there evidence that his true support exceeds 20% if my sample was a nationwide SRS?

Test used: ________________________ df = ________  P = ________
Answer: ___________________________________________________________________

7. (6)

In Dr. Norse’s Egg Drop Competition, 17% of Form V eggs cracked, but only 13% of Form VI eggs cracked. If the eggs are treated as SRS’s from two independent populations (30 in each form), is there evidence of a difference between the true propensities to crack?

Test used: ________________________ df = ________  P = ________
Answer: ___________________________________________________________________