4 Two educational researchers are investigating the relationship between personal ambitions and home location of students. The researchers classify students into those whose main personal ambition is good academic results and those who have some other ambition. A random sample of 480 students is selected.

1. One researcher summarises the data as follows.

   Observed		Home location
   \cline { 3 - 4 }	City	Non-city
   \multirow{2}{*}{Ambition}	Good results	102	147
   \cline { 2 - 4 }	Other	75	156

   Carry out a test at the \(5 \%\) significance level to examine whether there is any association between home location and ambition. State carefully your null and alternative hypotheses. Your working should include a table showing the contributions of each cell to the test statistic.
2. The other researcher summarises the same data in a different way as follows.

   Observed		Home location
   \cline { 3 - 5 }	City	Town	Country
   \multirow{2}{*}{Ambition}	Good results	102	83	64
   \cline { 2 - 5 }	Other	75	64	92

   (A) Calculate the expected frequencies for both 'Country' cells.
   (B) The test statistic for these data is 10.94 . Carry out a test at the \(5 \%\) level based on this table, using the same hypotheses as in part (i).
   (C) The table below gives the contribution of each cell to the test statistic. Discuss briefly how personal ambitions are related to home location.

   Home location \cline { 2 - 5 } City Town Country \multirow{2}{*}{Ambition} Good results 1.129 0.596 3.540 \cline { 2 - 5 } Other 1.217 0.643 3.816 Comment briefly on whether the analysis in part (ii) means that the conclusion in part (i) is invalid. This paper (3 questions) View full paper Q1 Q3 Q4