AMA2D02 Statistics in Society

Assignment 3


Instructions:

Upload and submit output file ”student number.pdf” (e.g. 19765432d.pdf)

Only One attempts are allowed for submission in which the final attempt will be graded

Late submission will NOT be accepted. Submission via email will NOT be accepted.

1 mark will be deducted for late submission or more than 1 attempt.


Information:

A random sample of 161 students are selected from Faculty A and Faculty B in the university. The test scores of Mathematics and English subject were recorded. Also, their years of study are recorded.

The data file “Testscore.csv” is given. The first column represents the test score of Mathematics.

The second column represents the test score of English, the third column represents the faculty of the students.


Task1

To study the performance Mathematics,

1. Find the mean and standard deviation for the test scores.

2. Construct a 95% confidence interval for the mean test score.

3. A random sample of 10 students from these 161 students with replacement, determine the standard error of the sample mean of 10 students. Hence, find the probability that the mean scores of these 10 students in Mathematics is more than 60.

4. Generating 100 random samples of size 20 from the population of 161 students, how many of the sample contains the population mean and show it with plot diagram in which those intervals do not contain the population mean in blue. [you are allowed to use R programme/Excel to generate random sample and plot diagram.]

5. By Central limit theorem, construct a 95% confidence interval for the difference in mean test score between Faculties A and B.


Task2

To study the overall performance including both Mathematics and English,

6. Find the mean and standard deviation for the test scores in English.

7. Construct a 95% confidence interval for proportion of students that the difference in the test scores of English and Mathematics who pass the test. Assume the passing marks for both English and Mathematics are 40.

[10 marks]