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Stats 2B03 Test #1

(Version 1)

October 22nd, 2013

Name:___________________________________________ (Last Name) (First Name)

Student Number:_____________________

Day Class

Duration: 75 Minutes Instructor: Childs

Maximum Mark: 21

This test paper consists of 20 multiple choice questions worth 1 mark each, and one question worth 1 mark on proper computer card filling. Marks will NOT be deducted for wrong answers (i.e., there is no penalty for guessing). QUESTIONS MUST BE ANSWERED ON THE COMPUTER CARD with an HB PENCIL. Answer all questions. You are responsible for ensuring that your copy of this paper is complete. Bring any discrepancy to the attention of your invigilator. Only the McMaster standard Calculator Casio fx-991 is allowed.

1. Consider the Minitab Output below which is a cross-tabulation table of the variables exercise (0 = none, = light, = moderate, = heavy) 1 2 3 and smoking status (0 = does not smoke, = smokes less than one pack per day, = smokes one or more packs per1 2 day) from the Databank data set. If two people are selected at random from the group of people summarized in the below output, find the probability that both people did not exercise and did not smoke.

Tabulated statistics: EXERCISE, SMOKING STATUS

Rows: EXERCISE Columns: SMOKING STATUS

0 1 2 All

0 17 14 7 38 1 15 18 5 38 2 8 3 2 13 3 7 2 2 11 All 47 37 16 100

Cell Contents: Count

(a) .35720 (b) .17860 (c) .03190 (d) .02890 (e) .02747

2. The mean number of serious accidents per year in a large factory is five. If the number of serious accidents follows a Poisson distribution, find the probability that in the current year there will be at least 2 accidents.

(2)

3. If is a standard normal random variable and D T ÐD Ÿ D Ÿ "Þ$"Ñ œ Þ%#!*" , find the value of

D".

(a)"Þ"' (b)Þ!% (c)Þ&$ (d)"Þ"' (e) Þ!%

4. The number of pounds gained during human pregnancy is a normal random variable with mean 30.23 pounds and standard deviation 13.84 pounds. If a mother is randomly selected, find the probability that she gained between 35 and 40 pounds during pregnancy.

(a)Þ"#)! (b)Þ#$)" (c)Þ"('$ (d)Þ!*%( (e)Þ$&*)

5. The number of pounds gained during human pregnancy is a normal random variable with mean 30.23 pounds and standard deviation 13.84 pounds. Fill in the blank. Only 10% of women gain more than _______ (how many?) pounds during pregnancy.

(a) 51.10 (b) 38.54 (c) (d)47.95 43.26 (e) 54.56

6. A researcher wants to estimate the mean age of a mother giving birth. A random sample of 16 women had an average age of 27.2 years, with a standard deviation of 1.3 years. Find a 99% confidence interval for the average age of a mother giving birth for the sampled population.

(a) (26.2423, 28.1577) (b) (26.3605, 28.0395) (c) (26.3628, 28.0372)

(d) (26.4441, 27.9600) (e) (26.6303, 27.7697)

7. A researcher wants to estimate the proportion of Canadians that are over the age of 65, accurate to within 2% using a 95% confidence interval. What is the minimum number of people that should be sampled?

(a) 2876 (b) 1294 (c) 3394 (d) 2401 (e) 1692

8. In order to estimate the average weight of a certain breed of dog, a researcher takes a sample of 45 dogs of that breed and produces the following 93% confidence interval

(26.6825, 29.5175). What was the sample standard deviation?

(a) 7.4288 (b) 6.1979 (c) 5.2535 (d) 4.8515 (e) 5.7805

9. The Birth data set contains the variable weeks, which is the length of pregnancy in weeks for a sample of women in North Carolina in 2001. Descriptive statistics for a sample taken from the weeks variable are given in the Minitab output below. Find a 95% confidence interval for the average length of pregnancy for all women in North Carolina in 2001. Descriptive Statistics: weeks

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 weeks 40 0 38.900 0.347 2.193 30.000 38.000 39.000 40.000

Variable Maximum weeks 43.000

(a) (38.4411, 39.3589) (b) (38.3161, 39.4839) (c) (38.1992, 39.6008)

(3)

10. Consider the below variables from the Databank data set. Which of these variables is measured on the nominal scale?

education level ! œno high school degree, " œhigh school graduate

# œcollege graduate, $ œgraduate degree

smoking status ! œdoes not smoke, " œsmokes less than one pack per

day

smokes one or more packs per day

# œ

exercise ! œnone, light, moderate, heavy" œ # œ $ œ

weight Weight in pounds

serum cholesterol Serum cholesterol level in milligram percent (mg%)

gender Mœmale, Fœfemale

marital status Mœmarried, Sœsingle, Wœwidowed, Dœdivorced

(a) education level, smoking status, exercise

(b) education level, smoking status, exercise, gender, marital status

(c) gender, marital status

(d) weight, serum cholesterol

(e) all of them

11. Consider the data set of systolic blood pressure readings that is summarized in the Minitab output below. Approximately how many of the people in the data set have a systolic blood pressure greater than 137?

Descriptive Statistics: SYSTOLIC

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 SYSTOLIC 85 0 129.78 1.35 12.47 110.00 119.50 128.00 137.00

Variable Maximum SYSTOLIC 163.00

(a) 75 (b) 21 (c) 64 (d) 25 (e) 43

12. Two people are selected at random from a group of 10 men and 15 women, to participate in an exercise study. Find the probability that at least one of them is a man.

(4)

13. Consider the following data set consisting of ages of men who are participating in an exercise study:

&&ß '$ß '&ß %"ß )(ß '!ß &)ß ($ß &$

Which of the following histograms was created by Minitab for this data set, i.e., which one of them is corrrect?

Age Fr e q u e n cy 90 80 70 60 50 40 4 3 2 1 0

Histogram of Age

Age Fr e q u e n cy 90 80 70 60 50 40 3.0 2.5 2.0 1.5 1.0 0.5 0.0

Histogram of Age

(a) (b) Age Fr e q u e n cy 90 80 70 60 50 40 3.0 2.5 2.0 1.5 1.0 0.5 0.0

Histogram of Age

Age Fr e q u e n cy 90 80 70 60 50 40 3.0 2.5 2.0 1.5 1.0 0.5 0.0

Histogram of Age

(c) (d) Age Fr e q u e n cy 90 80 70 60 50 40 3.0 2.5 2.0 1.5 1.0 0.5 0.0

Histogram of Age

(e)

14. autosomal Suppose that a disease is inherited via an recessive mode of inheritance. The

implications of this mode of inheritance are that the children in a family each have a

probability of of inheriting the disease. In a family of 8 children, find the probability that"% exactly 2 of them have the disease.

(5)

15. Systolic blood pressure readings were taken from 11 randomly selected people who have been recently diagnosed with hypertension, and are given below.

127 128 128 129 111 136 145 163 132 138 129ß ß ß ß ß ß ß ß ß ß

Which of the below stem and leaf plots is a correct stem and leaf plot for this data?

(a) Stem-and-leaf of Systolic N=11 (b) Stem-and Leaf Unit = 1.0

1 11 1 6 12 78899 (3) 13 268 2 14 5 1 15 1 16 3

-leaf of Systolic N=11 Leaf Unit = 1.0

1 11 1 (5) 12 78899 3 13 268 1 14 5 0 15 1 16 3

(c) Stem-and-leaf of Systolic N=11 (d) Stem-and Leaf Unit = 1.0

1 11 1 5 12 78899 (3) 13 268 1 14 5 0 15 1 16 3

-leaf of Systolic N=11 Leaf Unit = 1.0

1 11 1 (5) 12 78899 5 13 268 2 14 5 1 15 1 16 3

(e) Stem-and-leaf of Systolic N=11 Leaf Unit = 1.0

1 11 1 (5) 12 78899 5 13 268 2 14 56 1 15 1 16 3

16. The average length of stay in a chronic disease hospital for a certain type of patient is 60 days with a standard deviation of 15 days. Suppose that a group of these patients are randomly selected (you have to figure out how many people are in this group). For this group of patients a researcher calculates the probability that their average length of stay is less than 58 days, and finds that probability to be .2119. How many people are in the group?

(6)

17. Consider the following data set,

"%ß "(ß )ß &ß %ß $

Which of the below plots is a correct normal probability plot for this data set?

(7)

18. Consider the following data set,

"%ß "(ß )ß &ß %ß $

Calculate the coefficient of variation.

(a) 43.75 (b) 58.61 (c) 62.15 (d) 67.69 (e) 73.41

19. Systolic blood pressure readings were taken from 11 randomly selected people who have been recently diagnosed with hypertension, and are given below.

127 128 128 129 111 136 145 163 132 138 129ß ß ß ß ß ß ß ß ß ß

Which of the below boxplots is a correct modified boxplot for this data set?

sy

st

o

lic

170

160

150

140

130

120

110

Boxplot of systolic

sy

st

o

lic

170

160

150

140

130

120

110

Boxplot of systolic

(a) (b)

sy

st

o

lic

170

160

150

140

130

120

110

Boxplot of systolic

sy

st

o

lic

170

160

150

140

130

120

110

Boxplot of systolic

(c) (d)

sy

st

o

lic

170

160

150

140

130

120

110

Boxplot of systolic

(8)

20. Consider the data set that is summarized in the following histogram of weight by gender that was produced by Minitab.

WEIGHT

Fr

e

q

ue

nc

y

240 200

160 120

80 18 16 14 12 10 8 6 4 2 0

240 200

160 120

80

F M

0 0 0 5 7 16 15

1 1

3 12 13 12

4

0 0 Histogram of WEIGHT

Panel variable: GENDER

If one person is randomly selected from the data set summarized in the histograms above, find the probability that they are male, given that they weigh less than 160 pounds.

(9)

21. Correctly fill out the bubbles corresponding to your student number and the version number of your test in the correct places on the computer card.

(10)

Answers :(Version 1)

1. e b e a c a d c e 2. 3. 4. 5. 6. 7. 8. 9. 10. c

Figure

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