Download Statistics 151 (Fall 2009) Version 2 Lab Examination Date: Instructor

Statistics 151 (Fall 2009) Version 2
Lab Examination
Date:
Instructor: Allan Wesley
Instructions: Write your name and id number in the spaces indicated. Write your answers on
this sheet in the spaces provided. You may use your lab manual. For the tests state your
assumptions but you do not need to verify them. No text, notes or calculator allowed. The
ONLY allowed computer programs are Minitab and the Windows Calculator. CAREFULLY
READ THE QUESTIONS.
Total: 35 points
Student Name
Student Id Number
1. As part of the National Health and Nutrition Examination Survey conducted by the United
States Department of Health and Human Services, self reported heights and measure heights
were obtained for males aged 12-16. Listed below are the sample results
Subject
Reported
Heights
Measured
Heights
1
2
3
4
5
6
7
8
9
10
11
68
71
63
70
71
60
65
64
54
63
66
67.9
69.9
64.9
68.3
70.3
60.6
64.5
67
55.6
74.2
65
Is there sufficient evidence to support the assertion that the mean height reported by males aged
12-16 is higher than the mean measured height? Conduct an appropriate test using an α=0.05.
(5)
2. Suppose the diameter of a tree of a certain type is normally distributed with a mean of 19
centimeters (cm) and a standard deviation of 6.2 cm.
(a) Suppose that a selected tree has a diameter larger than 70% of these types of trees. What is
the diameter of this tree? (2)
(b) What is the probability that the diameter of a randomly selected tree will be between 16 and
22 cm in diameter? (3)
3. According to one report, when circuit boards used in the manufacture of DVD players are
tested, the long run percentage of defectives is 5%. If we take a sample of 25 circuit boards find
the probability that
(a) Exactly 22 are NOT defective. (1)
(b) 2 or less are defective. (2)
4. Eight pages were randomly selected from the book The Bear and the Dragon by Tom Clancy
and J.K. Rowling’s book Harry Potter and the Philosopher’s Stone. The Flesch Kincaid Grade
Level (1 means it is written at a grade 1 level, 2 that is was written at a grade 2 level and so on)
score was calculated for selected pages in the 2 books and is displayed below.
The Bear and
8.8
5.4
5.0
7.6
9.0
3.2
12.0
4.9
the Dragon
Harry Potter
and the
5.2
3.7
6.1
4.9
4.4
3.2
5.6
6.9
Philosopher’s
Stone
(a) Test using an α=0.10 if there is a significant difference in the mean grade levels between the
2 books. (5).
(b) Find a 98% confidence interval for the mean Flesch Kincaid Grade level of The Bear and the
Dragon. My uncle Bill, a big Tom Clancy fan thinks that this book is written at a grade 8 level.
Using only this confidence interval evaluate Bill’s assertion. (3)
(c) Calculate the mean and standard deviations for the Flesch Kincaid Grade level of both
books. Which book has the higher mean? (2)
5. Assume that the time until failure for these circuit boards follows an exponential distribution
with a mean of 60 months and a standard deviation of 60 months. If we take a sample of 36
circuit boards, find the probability that
(a) the AVERAGE time until the circuit fails is exactly 60 months. (1)
(b) the AVERAGE time until the circuit fails is more than 6 years. (3)
6. Clarinex is a drug used to treat asthma. In clinical tests of this drug, 1655 patients were
treated with 5-mg doses of Clarinex, and 35 of them experienced fatigue.
(a) Use a level of significance of 0.01 to test the assertion that the proportion of Clarinex users
experiencing fatigue is greater than the 1.2% rate for those not using Clarinex. (5)
(b) Dr. Bob is thinks that the proportion of Clarinex users who experienced fatigue is 1%.
Using a 97% confidence interval for the proportion of Clarinex users experiencing fatigue to
confirm or contest Dr. Bob’s assertion. (3)