Abe Mirza Part 1 Practice Problems Statistics

Abe Mirza

Part 1 Practice Problems

Statistics

Questions A. Determine whether the given value is a statistic or a parameter.

1. A sample of divers is selected, and the average age is 41.8 years.

2. After checking computer records for every commercial movie made last year the longest running time is found to be 187 minutes

3. All of the cities mayors are surveyed, and the 250 out of them are found to be democrat.

4. The average speed of 35 drivers on the highway.

5. The average IQs of the top 10 Miss Universe finalists.

Questions B. Determine whether the given values are from a discrete or continuous data set.

1. A math teacher counts 4 absent students

2. The weight of SUVs made in Japan.

3. The annual average rainfall in California.

4. The times taken for athletes to run 100m.

5. The numbers of chocolates in various 500g boxes.

Questions C. Identify which type of sampling of sampling is used: Random, Systematic, Cluster, Convenience, or Stratified.

1. At a local Mall a researcher ask every 10th passing by shoppers about the new security measure.

2. CNN is planning an exit poll in which 100 polling stations will be randomly selected and all voters will be interviewed as they leave the premises.

3. An engineering student measures the strengths of finger used to push buttons by testing family members.

4. An IRS researcher investigates cheating on income tax reports by surveying all waiters and waitresses at 20 randomly selected restaurants.

5. A marketing expert for MTV is planning a survey in which 500 people will be randomly selected from each age groups of 10-19, 20-29, and so on.

6. The author surveyed all of his students to obtain sample data consisting of the number of credit cards students possesses.

7. Fund-raisers for the college of Newport test a new telemarketing campaign by obtaining a list of all alumni and selecting every 1000th name on the list.

8. In a Gallup poll of 1045 adults, the interview subjects were selected by using a computer to randomly generate telephone numbers that were then called.

9. A market researcher has partitioned all Californian residents into categories of unemployed, employed full time, and employed part time. She is surveying 50 people from each category.

10. Motivated by a student who died from binge drinking. The College of South land conducts a study of students drinking by randomly selecting 10 different classes and interviewing all students in each of those classes.

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Question D.

There were six different stat classes that were offered last semester; one student was randomly selected from each class with his/her final score and the class average and standard deviation.

Joe got score of 83 when the class average was 71 with standard deviation of 6.5. Moe got score of 88 when the class average was 76 with standard deviation of 7.5. Nielo got score of 77 when the class average was 72 with standard deviation of 2.3. April got score of 82 when the class average was 72 with standard deviation of 5.5. Max got score of 82 when the class average was 71 with standard deviation of 5. Alex got score of 82 when the class average was 72 with standard deviation of 6.

Use the Z-score formula to answer the following questions:

a)Who did relatively better in the class than the rest? b)Who did relatively worse in the class than the rest? c)Who got scores that can be considered unusual?

Answers

Questions A. 1. statistic, 2. parameter, 3. parameter, 4. statistic, 5. statistic

Questions B.

1. Discrete, 2. Continuous, 3. Continuous 4. Continuous, 5. Discrete

Questions C.

1. Systematic

2. Cluster.

3. Convenience. 4. Cluster.

5. Stratified

6. Convenience.

7. Systematic.

8. Random.

9. Stratified 10. Cluster

Questions D.

Name

Joe Moe Nielo April Max Alex

a)Max

b) Moe

x

x

83

71

88

76

77

72

82

72

82

71

82

72

c) Nielo and Max

s

z xx

s

6.5

1.85

7.5

1.60

2.3

2.17

5.5

1.82

5

2.20

6

1.67

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Ungrouped Data

Mean Mode Median

A

B

C

D

E

F

G

23

33

46

129

33

321

461

39

49

78

156

41

319

782

32

42

64

145

49

231

643

66

76

132

160

56

265

132

58

68

116

119

85

541

126

42

52

84

134

24

442

184

37

47

74

170

73

358

274

49

59

98

98

94

149

398

47

57

94

144

74

333

394

32

42

64

135

23

301

464

162

82

329

156

152

44

149

288

147

231

136

149

152

333

138

256

Min

Q1

Q2

Q3

Max Range Box_Plot

St. Dev Variance

Est St. Dev

99% 99%

95% 95%

68% 68%

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Answers to Ungrouped Data

A

B

23

33

39

49

32

42

66

76

58

68

42

52

37

47

49

59

47

57

32

42

Mean Mode Median

Min Q1 Q2 Q3 Max Range Box_Plot

42.50 32 40.5

23 32 40.5 49 66 43

52.50 42 50.5

33 42 50.5 59 76 43

St. Dev Variance

Est St. Dev

12.90 166.50 10.75

12.90 166.50 10.75

C 46 78 64 132 116 84 74 98 94 64

85.00 64 81

46 64 81 98 132 86

25.81 666.00

21.5

D 129 156 145 160 119 134 170 98 144 135 162 152 147 136 152 138

142.31 152 144.5

98 134.5 144.5 154 170

72

17.78 315.96

18

E 33 41 49 56 85 24 73 94 74 23 82 44

56.50

52.5

23 37 52.5 78 94 71

24.55 602.82 17.75

F 321 319 231 265 541 442 358 149 333 301 329 149 231 149 333 256

294.19 149 310

149 231 310 333 541 392

105.19 11065.10

98

G 461 782 643 132 126 184 274 398 394 464 156 288

358.50

341

126 170 341 462.5 782 656

207.51 43061.36

164

99% 99%

95% 95%

81.21 3.79

68.31 16.69

91.21 13.79

78.31 26.69

162.42 7.58

136.61 33.39

195.64 88.99

177.86 106.76

130.16 -17.16

105.60 7.40

609.76 -21.38

504.57 83.81

981.04 -264.04

773.52 -56.52

68% 68%

55.40 29.60

65.40 39.60

110.81 59.19

160.09 124.54

81.05 31.95

399.38 189.00

566.01 150.99

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A.

Age(Month) 1 - 3 3 - 5 5 - 7 7 - 9 9 - 11 11 - 13

f

5

10

15

12 6 2

nf

Draw the

1. Histogram (write your observation)

Compute. 3. Mean?(Answ: 6.4 )

Grouped Data

m

f m

2

40

8

96

12

( f m) =

f m2

540 600

2 (f m ) =

2. Frequency polygon 4. Variance?( Answ 6.69 )

5. Standard deviation? (Answ 2.6)

0 99.7 % of data 14.2 ,

1.2 95 % of data 11.6 ,

6. Apply all three empirical rules.

3.8 68 % of data 9

B.

Scores

f

00-10

2

10-20

6

20-30

8

30-40

14

40-50

16

50-60

14

60-70

16

70-80

12

80-90

8

90-100

4

nf

m

f m

5

200 490

55 1040

( f m) =

f m2 1350 5000 17150 32400

2 (f m ) =

Draw the

1. Histogram (write your observation)

2. Frequency polygon

Compute.

3. Mean? (Answ 52.80)

4. Variance? (Answ 490.06)

5. Standard deviation? (22.14)

0 99.7 % of class 119.22 ,

6. Apply all three empirical rules.

8.52 95 % of class 97.08 ,

30.66 68 % of class 74.94

C.

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