Statistics and Probability Answers

The Dean the School of education, a University wants to determine whether there are statistically significant difference of opinion among the different cadres of academic staff members at the university concerning a proposed curriculum change in which postgraduate students are to be taught research methods on-line. Interviewing a sample of 313 members of the academic staff constituting 104 Lecturers, 131 Senior Lecturers, and 78 Professors, the Dean obtained the results shown in the following table:

Rank

Response

Lecturer

Senior Lecturer

Professor

Total

Against

47

34

14

95

Not committed

41

49

29

119

In support

16

48

35

99

Total

104

131

78

313

Compute a chi-square test for the above data and draw conclusion at α = .05                

 A University found that 20% of its students withdraw without completing the first semester courses. Assume that 6 students have registered for the course this semester. To compute the following questions use binomial probability distribution.

a.      Compute the probability that 2 or fewer will withdraw?

b.      Compute the probability that exactly 4 will withdraw?

c.       Compute the expected number of withdrawals?

d.     What is the variance of the number of withdrawals?

e.     What is the standard deviation of the number of withdrawals?

How many arrangement are there of the letters DISAPPOINT?

Question 5

a) Explain the significance of P(A or B) = P(A) + P(B) – P(A and B) as addition rule in probability. At what stage would P(A or B) = P(A) + P(B), and what is the rationale behind this? CR (5 marks)

b) Forty-eight percent of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Among Latino California registered voters, 55% prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. 37.6% of all Californians are Latino. Let C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first-degree murder. Let L = Latino Californians. Suppose that one Californian is randomly selected. Determine P(C/L) and explain the reason behind your answer. AN (7 marks)

c) Explain the dichotomy between mutually exclusive event and dependent event in a probability distribution.

Question 3

a) State the Poisson Equation and explain its significance to an industry AP (6 marks)

3

b) An average of 10 cars per minute pass through a toll booth during rush hour. Using the Poisson distribution, find the probability that less than 6 cars pass through the toll booth during a randomly chosen minute and explain the significance of your

AN (6 marks)?

c) The probability distribution of lunch customers at a restaurant is given in Table 2, you are required to calculate expected number of lunch customers, the variance, and the standard deviation. Explain the significance of your answer in each case.

EV (7 marks)

Total Marks: 20

Table 2

Number of customers

Probability

100

110

118

120

125

0.2

0.3

0.2

0.2

0.1

Question 2

You are required to use the data provided in Table 1.0 to determine:

a) The modal price in $US AN( 7 marks)

b) The standard deviation AN( 7 marks)

c) The skewness of frequency distribution and explain the significance of the results in terms the direction of your findings. AN (6 marks)

Explain the significance of your answer in each case.

Table 1.0

Price ($US)

Frequency

1.0-1.01

1.05-1.09

1.10-1.14

1.15-1.19

1.20-1.24

1.25-1.29

4 6 1 0 15 8 5

Total Marks: 20

Question 1

 a) Discuss how statistical data can support policy making

b) Examine a dichotomy between qualitative and quantitative data in research

c) What is your view on the significance of descriptive and inferential

statistics?

1.      State the null hypothesis of the following:

A. There is a significant relationship between job satisfaction and job performance.

B. There is a significant difference between the performance of male and the female employees in a company.

C. There is a significant relationship between the amount of hours for studying the lessons and the academic performance of freshmen students in the University.

In a box are 2 balls - one white and one yellow. Two balls are picked one at a time with replacement. Let X be the random variable representing the number of white balls. Find the values of the random variable X.

The time taken X by a garage to repair a car is a continuous rv with pdf f(x) = { 3x 4 (2 − x); 0 ≤ x ≤ 2 0; elsewhere If, on leaving his car, a motorist goes to keep on an engagement lasting for a time Y, where Y is a continuous rv independent of X, with pdf f(y) = { 1 2 y; 0 ≤ y ≤ 2 0; elsewhere . Determine the probability that the car will not be ready on his return.