Broward College

Math Dept.

Statistics STA2023

Review Test # 1

 

1-)  Determine whether the given values are statistics or a parameters. Determine the population and the sample (if any):

   

  a-) In a FOX News poll conducted 5/15-5/17-2011, a sample of 910 voters were asked if they approve the job of the president Barack Obama. 55% of the respondents approve the job of the president.(taken from http://www.realclearpolitics.com/polls/) During the presidential election in 2008, 52.9% of the voters voted for Barack Obama (“http://en.wikipedia.org/wiki/United_States_presidential_election,_2008”)

 

     b-) According to Census 2000 (“http://www.nationalatlas.gov/articles/people/a_race.html”), 281.4 million people resided in the United States at that time, 12.5 % were Latino, and 12.3 % were African-Americans.

 

 

 

2-) Engineers must consider the breadth of male heads when designing motorcycle helmets. A random sample of 30 men was selected and their head breadth is shown in the table:

3.4

4.6

5.2

5.6

5.8

6.5

6.6

6.9

7.5

9.5

3.4

4.7

5.1

5.4

5.8

6.4

6.6

6.8

7.0

7.8

4.5

4.9

5.0

5.4

5.6

6.3

6.5

6.7

6.9

7.6

 

a-) Make a Box-Plot and check for possible outliers.

b-) Describe the distribution using the information obtained in a-1).

 

 

 

3-)  A sample of 30 individuals was randomly selected. Their IQ is shown in the table:

 

87

107

103

96

98

91

91

114

87

91

86

101

106

91

89

101

100

115

88

117

112

101

127

99

102

115

110

108

93

87

 

 

a-) Create classes. Make a frequency table showing class limits.

b-) Draw a relative-frequency histogram

c-) Draw a Ogive (cumulative frequency distribution

d-) Describe the distribution.

 

4-)a-) Laura is playing with three dice. On her next move she needs to throw a sum smaller than 8. What is the probability that Laura will roll a sum smaller than 8?

b-)Assume that you want to simulate the rolling of three dice.  Describe the simulation using RandomInt(). Simulate the rolling of three dice 100 times, perform the experiment, and find the observed number of values (O) smaller than 8.  Could the values obtained in “a” and “b” be different? Explain why?  Find the residual. 

 

 

5-) A Gallup poll conducted in November 2002 examined how people perceive the risks associated with smoking. The following table summarizes data on smoking status and perceived risk of smoking and is consistent with summary quantities published by Gallup. Calculate the marginal distribution:

 

Smoking Status

Very Harmful

Somewhat Harmful

Not too Harmful

Not at All Harmful

 

Current Smoker

60

30

5

1

 

Former Smoker

78

16

3

2

 

Never Smoked

86

10

2

1

 

 

 

 

 

 

 

 

a-) What is the probability that a randomly selected U.S. adult is NOT a Former Smoker?

b-) What is the probability that two randomly selected U.S. adults both are Former Smoker?

c-) What is the probability that a randomly selected U.S. adult views smoking as very harmful under the condition that the selected adult is a Current Smoker?

d-) What is the probability that a randomly selected U.S. adult views smoking as very harmful given that the selected individual never smoked?

e-) What is the probability that a randomly selected U.S. adult views smoking as very harmful OR that the selected individual is a former smoker?

f-) What is the probability that a randomly selected U.S. adult is a current smoker AND that the selected individual considers smoking as very harmful?

g-) Are the events Former Smoker and Very Harmful independent?