STAT170: Statistics - Regression Analysis

Solution Code : 1HJE

Question:Statistics

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Statistics Assignment

Assignment Task

Question 1 A researcher decided to investigate the relationship between student enrolment numbers and teaching staff in remote schools. The following Minitab output was obtained using information recorded on student enrolment numbers and teaching staff in 2014 at 25 very remote schools in Australia. Use this to answer parts a. and b.

Comment on the validity of each the three assumptions for linear model by referring to each of the plots above:
The largest residual was for Goodooga Central School which had the equivalent of 9.4 teaching staff in 2014 and 35 enrolments in 2014. Use this information, and the Fitted Line Plot above, to calculate the residual for Goodooga Central School and explain clearly what is unusual about Goodooga Central School.

Question 1 continued The following output was obtained using information on 24 of the very remote schools, (excluding Goodooga Central), from 2014. Use this information to answer part c.

Why do you think that Goodooga Central school was excluded from this analysis?
Use an appropriate hypothesis test to determine whether the number of student enrolments at very remote schools in 2014 was a useful predictor of the number of teaching staff:

Question 1 continued A previous study of the 24 schools from parts c. and d. had been conducted in 2008. The following output was obtained using some of the information recorded on these 24 schools in 2008. Use this output, together with your answers to parts c. and d. to answer the remainder of this question.

In 2008, did the school with the highest number of student enrolments also have the highest number of teachers?
How many students (approximately) were enrolled at the school with the highest number of teachers in 2008?
Explain why the model for predicting teaching staff in 2014 will give more reliable predictions than the model for predicting teaching staff in 2008.
Make the following predictions, if possible. If not, explain why your predictions would not be valid.

Predict the number of teachers in 2008 at a very remote Australian school which had 50 students enrolled.
Predict the number of teachers in 2014 at a very remote Australian school which had 50 students enrolled.
Predict the number of teachers in 2014 at a very remote Australian school which had 150 students enrolled.

Question 2 An educational researcher carried out a study into standardised examinations for high school students. 150 Year 7 students were randomly selected from schools across Australia in 2011 and various information was recorded on these students over a four year period. Some of the variables recorded were:

The data are stored in the Excel file: ExamMarks.xlsx which is on iLearn. Use this data file to complete Question 2. Each part of this question must be labelled and must be presented in order and must be neatly word processed. Untidy work wll not be marked. Each part (a., b. and c.) should be answered by a different student from your group. Each part of this question uses a different section of the data set which should be extracted (either by sorting the data or splitting the worksheet). Each part asks about the difference between average marks for a particular group of students. Since the worksheet contains data on both English and Mathematics marks, each part should address both English and Mathematics marks (ie. one hypothesis test on English marks and one hypothesis on Mathematics marks for each part). Minitab output for these analyses, along with any other appropriate graphical output, should be cut and pasted neatly into the space provided for each part. Please note that output that is not clearly labelled will not receive any marks (eg. Group 1 is not a clear label whereas Co-educational School is a clear label). On the following page provided for each part, a report on these analyses should be written up. One report only is required for each part, with the report addressing both English and Mathematics scores in regard to the Research Question. Reports should follow the format described in the report writing document on iLearn, with particular attention to the section ‘A Short Guide to Report Writing for STAT170 students’. Each report will have an Introduction, a Methods section, a Results section and a Conclusion as outlined in the report writing document. Reports should not be more than one A4 page in length. Research Questions for Q2:

Amongst students attending boys only schools, did the average marks on standardised exams change significantly between Years 7 and 11?

Amongst Year 11 students, were the average marks on standardised exams for students at Government schools different to the average marks for students at Independent schools?

Amongst Year 7 students at were the average marks on standardised exams for for students at boys only schools different to the average marks for students at girls only schools?

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Solution:

Part a Output:

Part a Report Introduction: The main objective of this section is to determine wehthe there is a significant difference in the average marks on standardised exams change significantly between Years 7 and 11. The average marks scores by the students in boys only shool is 54.87813 in year 7 and 57.11384 in year 11. Methods: In order to test the claim, we perform independent sample t test. Here, the independent variable is the class 7 and class 11 and the dependent variable is the standardized scores. Since two groups are independent, we can perform independent sample t test Results: The value of t test statistic is -0.91825 and its corresponding p – value is 0.3607 > 0.5, indicating that there is a sufficient evidence to reject the claim Conclusion: Here, we fail to support the claim that there is a significant difference in the average marks on standardised exams change significantly between Years 7 and 11 Part b Output:

Part b Report Introduction: The main objective of this section is to determine wehthe the average marks on standardised exams forstudents at Government schools different to the average marks for students at Independent schools. The average marks scores by the students in government schools is 60.83673 and 58.35 in independent schools. Methods: In order to test the claim, we perform independent sample t test. Here, the independnet variable is the government school and independent school and the dependent variable is the standardized scores. Since two groups are independent, we can perform independent sample t test Results: The value of t test statistic is 0.9744 and its corresponding p – value is 0.3323 > 0.5, indicating that there is a sufficient evidence to reject the claim Conclusion: Here, we fail to support the claim that there is a significant difference in the average marks on standardised exams for students at Government schools different to the average marks for students at Independent schools Part c Output:

Part c Report Introduction: The main objective of this section is to determine wehthe average marks on standardised exams for for students at boys only schools different to the average marks for students at girls only schools at year 7. The average marks scores by the students in boys schools is 54.87813 and 59.67 in girls schools. Methods: In order to test the claim, we perform independent sample t test. Here, the independent variable is the boys only school and girls only school and the dependent variable is the standardized scores. Since two groups are independent, we can perform independent sample t test Results: The value of t test statistic is -2.022 and its corresponding p – value is 0.0457 < 0.5, indicating that there is a sufficient evidence to support the claim Conclusion: Here, we support the claim that there is a significant difference in the average marks on standardised exams for for students at boys only schools different to the average marks for students at girls only schools at year 7

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