(a) The ministry of education is considering funding pre-school education. Before making their recommendations, administrators take a random sample of 100 students from various areas to compare the performance of students in algebrs between those who attended pre-school and those who did not. The results are summarised in the table below: Below Grade Level | At Grade Level Advanced 29 Pre-school 12 16 No pre-school 18 11 14 i. Based on the data a the table, and without conducting any significance test, would you say there is an association between attending pre-school and performance in algebra? ii. Calculate the x statistic and use it to test for independence between attending pre-school and performance in algebra at two appropriate significance levels. What do you conclude?

MATLAB: An Introduction with Applications
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(a) The ministry of educntion is considering funding pre-school education. Before
making their recommendations, administrators take a random sample of 100
students from various areas to compare the performance of students in algebra
between those who attended pre-school and those who did not. The results are
summarised in the table below:
Below Grade Level
12
At Grade Level
29
Advanced
Pre-school
16
No pre-school
18
11
14
i. Based on the data a the table, and without conducting any significance
test, would you say there is an association between attending pre-school
and performance in algebra?
ii. Calculate the x? statistic and use it to test for independence between
attending pre-school and performance in algebra at two appropriate
significance levels. What do you conclude?
(13 marks)
You have been asked to design a cluster random sample survey on public sector
workers to examine whether satisfaction on working conditions of employees
varies between different job types.
i. Discuss in no more than three sentences how you will choose your sampling
frame. Also discuss the limitation(s) of your choice.
ii. Propose two relevant clusters. Justify your choices.
iii. Discuss in no more han two sentences, how selection bias could affect the
results in the context of this survey.
v. Briefly discuss the statistical methodology you would use to analyse the
collected data.
Transcribed Image Text:(a) The ministry of educntion is considering funding pre-school education. Before making their recommendations, administrators take a random sample of 100 students from various areas to compare the performance of students in algebra between those who attended pre-school and those who did not. The results are summarised in the table below: Below Grade Level 12 At Grade Level 29 Advanced Pre-school 16 No pre-school 18 11 14 i. Based on the data a the table, and without conducting any significance test, would you say there is an association between attending pre-school and performance in algebra? ii. Calculate the x? statistic and use it to test for independence between attending pre-school and performance in algebra at two appropriate significance levels. What do you conclude? (13 marks) You have been asked to design a cluster random sample survey on public sector workers to examine whether satisfaction on working conditions of employees varies between different job types. i. Discuss in no more than three sentences how you will choose your sampling frame. Also discuss the limitation(s) of your choice. ii. Propose two relevant clusters. Justify your choices. iii. Discuss in no more han two sentences, how selection bias could affect the results in the context of this survey. v. Briefly discuss the statistical methodology you would use to analyse the collected data.
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