ICEF 2003/2004

STATISTICS

FIRST YEAR

EXAM

Section II Part a Problems 1  5

Spend about 65 minutes on this part of the exam

Percent of Section II grade 75%

NAME
GROUP

Problem 1

During the 1950s, radioactive waste leaked from a storage area near Hanford, Washington, into Columbia River nearby. For nine counties downside in Oregon, an index exposure X was calculated (based on distance from Hanford, and distance of the average citizen from the river, etc). The cancer mortality Y was also calculated (deaths per 100,000 persons years, 1959-64), giving the following data (Fadeley 1965, via Anderson and Sclove, 1978):

County	Radioactive Exposure X	Cancer Mortality Y
Clastop	8.3	210
Columbia	6.4	180
Gilliam	3.4	130
Hood River	3.8	170
Morrow	2.6	130
Portland	11.6	210
Sherman	1.2	120
Umatilla	2.5	150
Wasco	1.6	140

From this data, summary statistics were computed:

.

1. Calculate the regression line for predicting Y from X.

2. Interpret the slope in the context of this situation.

3. Estimate the cancer mortality if X were 5.0.

4. The sum of squares of residuals of regression in (a) is 1487.3. To what extent does this data prove the harmfulness of radioactive exposure?

NAME
GROUP

Problem 2

The Alps Mountain Rescue Service wishes to study the behavior of lost hikers. If more were known about the direction in which lost hikers tend to walk, then more effective search strategies could be devised. Two hundred hikers selected at random from those applying for hiking permits are asked whether they would head uphill, downhill or remain in the same place if they became lost while hiking. Each hiker in the sample was also classified to whether he or she was an experienced or novice hiker. The resulting data are summarized in the following table.

	Direction
	Uphill	Downhill	Remain the Same Place
Novice	20	50	50
Experienced	10	30	40

Do these data provide convincing evidence of an association between level of hiking expertise and the direction the hiker would head if lost?

NAME
GROUP

Problem 3

It is reported that the lake water contains 0.5g of salt per 1 litre, with a standard deviation 0.1g.

1. In order to check this statement, 20 samples of water were chosen and the mean amount of the salt in a sample of one litre was 0.57g. Is the report of the salt content correct?

2. It was discovered later on, that in fact only 10 samples of water were chosen and other 10 measurements just duplicate the first 10. Does your conclusion change?

NAME
GROUP