Quantitative Methods

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CONTENT

Question 1

Question 2

Question 3

Question 4

Question 5

BIBLIOGRAPHY

QUESTION 1

Class Interval of iPods

Freq f

Class Midpt, x

20-50

44100

50-80

608400

80-110

17728900

110-140

250000

140-170

384400

=3440

=19015800

1.2.1

1.2.2

1.2.3.

1.3.1

= (k/100)(n)

= (65/100)(40)

= 26th position

65th percentile

= L+[(P-cf)/f (U-L)]

= 80.5+[(26-18)/14 (110.5-80.5)]

= 80.5 + 17.14

= 97.14 or 97

1.3.2

Q1 = 1(N)th value

= (1(40))/4 th value

= 10th value

10th value is in the interval 50.5 – 80.5

Therefore Q1 is (50.5 – 80.5)

= L+ h/f(iN/4-c)

= 50.5+ 30/12(1(40)/4-6)

= 50.5 + 10

= 60.5 or 61

Q3 = 3(N)th value

= (3(40))/4 th value

= 30th value

30th value is in the interval 80.5 – 110.5

Therefore Q3 is (80.5 – 110.5)

= L+ h/f(iN/4-c)

= 80.5+ 30/14(3(40)/4-18)

= 80.5 + 25.71

= 106.21

The Quartile Deviation = (Q3 – Q1)/2

= (106.2-60.5)/2

= 22.85 or 23

QUESTION 2

2.1 Mean (μ)

= X/N

= 10833/12

= 902.75

Standard Deviation (σ) = √(〖(X-M)〗^2/(N-1))

=√(143420/(12-1))

= √13038.21

= 114.185

= P(X < 800)
= P(X -)/ < (800 - 902.75)/114.185
= P (Z< -0.899855)
= .1841
1 billion = 1000 million
μ = 902.75
σ = 114.185
standardise x to z = (x - μ) / σ
P(x > 1000) = P (z > (1000-902.75) / 114.185)

= P (z > 0.8517) = .1977

We know from the standard normal that

P (Z < z) = 0.95 = P(Z > z) = 0.05

when z = 1.644854

x = μ + z * σ

x = 902.75 + 1.644854 * 114.185

x = 1090.568 or 1091

QUESTION 3

H0: There is no evidence of a change in the market shares of car rental firms

H1: There is evidence of a change in the market shares of car rental firms

= 0.05

Reject H0 if the calculated X2 > 15.507

df = (k-1)(r-1) = (5-1)(3-1) = 8

CONTINGENCY TABLE:

CONTINGENCY TABLE

x^2= ((f0 – fe)2)/fe

28.91

0.041

24.78

0.002

16.84

0.593

17.47

0.691

0.140

30.13

0.042

25.83

0.309

17.55

0.012

18.21

0.176

0.404

31.96

0.000

27.39

0.248

18.61

0.701

19.31

0.147

0.068

3.575

# Essay About P-Cf And U-L

Essay, Pages 1 (208 words)

Latest Update: April 2, 2021

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P-Cf And U-L. (April 2, 2021). Retrieved from https://www.freeessays.education/p-cf-and-u-l-essay/