Question 3 a) There are 500 students enrolled in statistics course this year. The lecturer takes a random sample of 100 students and found that the proportion of students who attend the online virtual classes was 78%. Use a level of significance of 0.05.

(i) Find the standard error of the sampling distribution of sample proportion. (3 marks)

(ii) Construct a 95% confidence interval for population proportion. (4 marks)

(iii) The attendance rate was 80% last year. The lecturer claims that the attendance rate of the students this year has changed. Based on Question 3a) (ii), do you think the lecturer claims was true? Explain. (2 marks)

(iv) Assume infinite population, find the sample size needed if the error is at most 1%. (3 marks)

b) The time spent on viewing the recorded lecture follows a normal distribution with a mean time of 70 minutes with a standard deviation of 25 minutes. The lecturer claims that the average time spent on viewing the recorded lecture is less than 60 minutes. To test the lecturer's claim, a random sample of 30 students was taken which showed an average time spent on viewing the recorded lecture is 57 minutes.

(i) Find the probability that the average time spent on viewing the recorded lecture is less than 57 minutes. (4 marks)

(ii) Suppose the management wished to have a 99% confidence that the estimated average time spent on viewing the recorded lecture to be differed by no more than 10 minutes. Does the sample size large enough to satisfy the management requirement? Justify. (3 marks)

(iii) Test the lecturer's claim at 0.01 level of significance. (6 marks) [Total: 25 marks]

AAMS2613 PROBABILITY AND STATISTICS

Question 4

a) The following data show the average time spent on outdoor activities per day, and the examination score for 10 students.

Average time spent (hours)	0	0.5	1	1	1.5	1.5	2	2	2.5	3
Examination score (%)	85	90	70	80	75	80	70	65	64	60

(i) Identify the dependent and independent variables. (2 marks)

(ii) Compute the correlation coefficient. Comment on the relationship between the average time spent on outdoor activities and the examination score. (5 marks)

(iii) Form the least squares equation. (5 marks)

(iv) Predict the score if a student selected at random spent an average of 3.5 hours on outdoor activities per day. Is the prediction reliable and accurate? Explain. (4 marks)

(v) Comment on whether the Spearman rank correlation coefficient should be used as an approximation to estimate the correlation between average time spent on outdoor activities per day and student's score in examination. Rank the examination score. (4 marks)

b) Find the total number of possible ways to arrange 3 digits even numbers that greater than 750 from the integers 4, 5, 6, 7 and 8 if repetition is allowed? Shows your workings. (2 marks)

c) Two letters are selected at random from the word COUNTING. Find the number of possible combinations of letter that without the letter of N. (3 marks)

[Total: 25 marks]