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BUSN1009 Quantitative Methods

tag 0 Download 2 Pages / 491 Words tag 17-06-2021

Question:

A city’s telephone book lists 100 000 people. If the telephone book is the frame for a study, how large would the sample size be if systematic sampling were done on every 200th person

If a university employed 3500 academic staff, and a random sample of 175 academic staff was selected using systematic sampling, what value of k was used? Between what two values would the sampling selection process have started? Where would a frame for this sampling of academic staff been obtained?

Compute the 20th percentile, the 60th percentile, Q1, Q2, Q3 and IQR for the following data.

470, 320, 146, 204, 800, 280, 957, 298, 445, 356, 450, 786, 964, 918, 849, 820

A data set contains the following eight values.

4 3 0 5 2 9 4 5

  1. Calculate the sample variance.
  2. Calculate the sample standard deviation.

According to a Human Resources report, a worker in the IT industry spends on average 419 minutes (or 6.98 hours) a day on the job. Suppose the standard deviation of time spent on the job is 27 minutes. a. If the distribution of time spent on the job is approximately bell shaped, between what two times would 68% of the data fall? 95%? 99.7%?

Use the values in the following contingency table to solve the equations given.

 

A

B

C

X

42

48

36

Y

54

30

18

Z

21

39

12

 P(A) = ___ c.P(A Ç X) = ___  e. P(A È C) = ___

  1. P(Z) = ___ d.P(B ÇZ) = ___ f. P(A Ç B)

Convert the following contingency table to a probability matrix to solve the equations given.

 

D

E

A

16

8

B

10

6

C

8

2

  1. P(A) = ___ c. P(A ÇE) = ___
  2. P(E) = ___ d. P(A ÷E) = ___

According to the ABS, 73% of women aged 25 to 54 participate in the labour force. Suppose that 78% of the women aged 25 to 54 are married. Suppose also that 61% of all women aged 25 to 54 are married and are participating in the labour force. What is the probability that a randomly selected woman aged 25 to 54:

  1. is married or is participating in the labour force
  2. is married or is participating in the labour force but not both
  3. is neither married nor participating in the labour force?

Given P(A) = .40, P(B) = . 25, P(C) = .35, P(B | A) = . .25 and P(A | C) = .80, solve the following.

  1. P(A ÇB) = ___
  2. P(A ÇC) = ___
  3. If A and B are independent, P(A ÇB) = ___
  4. If A and C are independent, P(A ÇC) = ___

Use the values in the contingency table to solve the equations given.

 

 

Variable 1

Variable 2

 

E

 

F

A

 

85

 

75

B

 

40

 

55

C

 

40

 

85

D

 

95

 

25

  1. P(F) = ___
  2. P(B ÈF) = ___
  3. P(D ÇF) = ___
  4. P(B | F) = ___
  5. P(A ÈB) = ___
  6. P(B ÇC) = ___
  7. P(F | B) = ___
  8. P(A | B) = ___
  9. P(B) = ___
  10. Based on your answers to these calculations, parts a, d, g and i, are variables 1 and 2 independent? Why or why not?
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