Question 1

The data set marks.xls introduced in Assignment 2 contains data on performance of a group of students in a university course. We are now interested in investigating the

exam performance of these students.

1. Assume the data set represents a random sample of all students enrolled in a particular course over a five year period. Estimate the mean \(\mu \) and standard deviation \(\sigma \) of exam results for the wider student population.
2. Use the results from (a) to obtain a 90% confidence interval for the mean exam mark m the wider student population.
3. Justify the use of the confidence interval formula you used in part (b).
   We are interested in whether Australian residents perform better on the exam than non-Australian residents.
4. Calculate separately; the sample mean exam marks for Australian residents and non-Australian residents.
5. Calculate the corresponding standard deviations.
6. Using the results from (d) and (e) test whether there is evidence that the mean exam mark for Australian residents is higher than the mean exam mark for non-Australian residents.

Question 2

Using the data set marks.xls we consider now the breakdown of students according to gender, country of residence and enrolling faculty.

1. Produce a contingency table displaying frequencies of male students only broken down according to country of residence and enrolling faculty.
2. Repeat part (a) for female students only.
3. Determine the proportion of
   1. female students in the group.
   2. male students from Australia enrolled through the business faculty.
   3. science faculty students who are female.
4. Making appropriate assumptions (state them), determine a 95% confidence interval for the proportion of overseas resident student in the course population.

Question 3

1. What is a lurking variable?
2. How does the central limit theorem differ from the law of large numbers?
3. Why do sample means usually differ from population means in simple random samples?
4. Why do sample means usually differ from population means in voluntary response samples?
5. What is the difference between a parameter and a statistic?
6. Why is the Central Limit Theorem important in statistics?
7. What is meant by the sampling distribution of a mean?
8. Telephone surveys can record very high non-response rates through people refusing to participate and people not being home. In about 30 words, identify- the major problem associated with the validity of the results of surveys of this type.
   Question 4
   A union official claimed that 40%of trucks carry too heavy a load. In random spot checks, the Main Roads Department found 17 of the 60 trucks tested were carrying too heavy a load. Does the sample result suggest that the union official's claim is exaggerated (too large)? Perform an appropriate hypothesis test. Calculate the p-value. Make an appropriate conclusion in the context of these data.
   Question 5
   Using hospital and agency records, six pairs of identical twins. one of whom was adopted at birth and the other of whom was in foster care for at least, two years. All the twins are now five -years old. All twins are tested with the Wechsler Intelligence Scale for Children (WISC) with the following results:

   Twin Pair	Adopted Twin	Foster-Care Twin
   1	105	103
   2	99	97
   3	112	105
   4	101	99
   5	124	104
   6	100	110
   7	110	104
   8	116	106

   
   Is there evidence of a difference in the average test results of the adopted twin and the foster care twin?
   1. Use a parametric test to answer this question.
   2. Use a nonparametric test to answer this question.
   3. Comment on any differences in the results of these tests.

Price: $27.24

Solution: The downloadable solution consists of 13 pages, 1424 words and 4 charts.
Deliverable: Word Document