QS 381 Winter 2002. Exam 1. January 18,2002 Time: 50 minutes. Put name on top of paper.

(1) During a run of sockeye salmon in lake Washington, a study was made of  the number of fish  passing through the Chittenden Locks fish ladder. One objective of this study was to determine the percentage of days that more than 425 fish  used the ladder. Suppose the mean for the data was 375 fish per day and the standard deviation was 30 fish.
(a) (8 pts)What can you say about the percentage of days that more than 425 fish used the ladder?
 
 
 (1) (a) at most 36% , k=(425-375)/30 = 1.67, 1-1/k^2 = 0.64, 1-0.64=0.36


 
 

(b) (8 pts)What is your answer to part (a) if you know that the relative frequency distribution for the data is bell-shaped and the standard deviation is 25 fish?
 
 (b) around 2.5%, where 95% of the data fall within 2 SD’s, 1-0.95 = 5/2 = 0.025
 
 
 
 
 
 
 

(2) Use the information from the following data set to complete the table.(7 pts)
 

Measurement Class

Relative Frequency

Frequency

Cumulative Frequency

0 <= x < 2

0.10

20

20

2 <= x < 4

0.15

30

50

4 <= x < 6

0.05

10

60

6 <= x < 8

0.45

90

150

8 <= x < 10

0.25

50

200

Draw the following for these data:
(a)(5 pts) frequency histogram
(b)(5 pts) frequency polygon
(c) (5 pts) relative frequency histogram
(d) (5 pts) frequency ogive
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

(e) (5 pts) Compute the sample mean
  Sum(x*f)/Sum(f) where x = midpoint

  (1*20+3*30+5*10+7*90 + 9*50)/200 = (20+90+50+630+450)/200 = 1240/200 = 6.2
 
 

(3) Define the kind of sampling and the type of data for each of the following. Give a reason for your answer.

(a) (4 pts) The density of E. coli in 1cc samples of saliva from 40 male and 25 female patients in Harborview medical center.
 
 
                        stratified sampling, with two strata, male and female; ratio data

(b) (4 pts) The size of fish caught by 120 anglers sampled through binoculars from by an observer at Matthews Beach on Lake Washington.
                              convenience sampling (only those angler's visible from that point) could also argue random
                               sample is ordinal, could be in categories small, medium or large, rankable but no intervals
 
  (c) (4 pts) The diameter at breast height (DBH) of 20  tree samples apiece taken from each of  3 chosen  stands at Pack Forest, Washington (Note: there are more than 3 stands at Pack Forest).
 
 Cluster sampling, because only some stands chosen. ratio data (true 0)
 
 

(d) (4 pts) The barometric pressure taken every quarter hour over a 10 day period in May on the UW Campus.
 
 Systematic sample, interval measure. I'm not sure if it is ratio. Accept either answer.

***If you wrote interval and only got partial credit, return your exam to Maureen for credit**** 

(4) Wildlife biologists trapped field mice in a particular field using an experimental trap. They were interested in how long it would take the mice to escape from the trap. Ten mice captures were observed.  Their times to escape (in minutes) are recorded below. The N's represent two rats that had still not escaped after 3 hours. The data are:
100, 38 , N , 122 , 95 , 116 , 56 , 135 , 104 , N
(a) (6 pts) Can the mean be calculated for this data set? If the answer is yes, report the value. If the answer is no, explain why not.
 
 (4)  (a) No, you need all the values of all the data points to calculate the mean
 
 

(b) (6 pts) Can the median be calculated for this data set? If the answer is yes, report the value. If the answer is no, explain why not.
  The data can be ordered, and the  median taken from the ordered data:

38        56        95        100      104      116      122      135      N         N

 
 
 

(5) A researcher is interested in the variability in leaf size (in cm) on a particular bigleaf maple tree early in the spring. He collected the following 10 data points, shown in the stem and leaf diagram.   Leaf units are in tenths. Note there are more than one kind of leaf in this problem. For these data find:
1 | 1 = 1.1

Stem

Leaf

0

3 1 5

1

1 0

2

2 1 2

3

1 8

(a)(4 pts) the mean
 
 (5) a) mean = 1.64

(b) (4 pts) the mode
 
 b) mode = 2.2

(c) (4 pts) the range
 c) range = 3.7
 

(d) (4 pts) the median
 
 d) median=1.6
 

(e) (8 pts) Draw a box and whisker diagram for these data above the following line:
 
 e) maximum =3.8, min=0.1, Q1=0.5,Q3=2.2
 
 
 
 
 
 

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