6. A student, considering options for the future, collects data on education and salary. The table below shows the highest level of education attained and the salary bracket of a random sample of 664 people. By conducting a chi-squared test for independence, the student investigates the relationship between the highest level of education attained and the salary earned.

1. State the null and alternative hypotheses.
2. The table below shows the expected values. Calculate the value of \(k\).

   Expected values	Fewer than 5 GCSE	5 or more GCSE	3 A Levels	University degree	Post graduate qualification
   Less than £20000	\(k\)	24.23	26•19	35.46	10.57
   £20000 to £60000	49.40	103.67	112.02	151.68	\(45 \cdot 23\)
   More than £60000	10.05	21.09	\(22 \cdot 79\)	30.86	9.20

3. The following computer output is obtained. Calculate the values of \(m\) and \(n\).

   Chi Squared Contributions	Fewer than 5 GCSE	5 or more GCSE	3 A Levels	University degree	Post graduate qualification
   Less than £20000	3.604530799	\(m\)	1.46165	1.5686	0.03098
   £20000 to £60000	0.007272735	0.72535	4E-06	0.07264	0.50396
   More than £60000	\(4 \cdot 946619863\)	0.03897	169081	\(0 \cdot 55498\)	\(n\)

   X-squared \(= 19 \cdot 61301 , d f = 8 , p\)-value \(= 0 \cdot 0119\)
4. 1. Without carrying out any further calculations, explain how X-squared \(= 19 \cdot 61301\) (the \(\chi ^ { 2 }\) test statistic) was calculated.
   2. Comment on the values in the "Fewer than 5 GCSE" column of the table in part (c).
5. The student says that the highest levels of education lead to the highest paying jobs. Comment on the accuracy of the student's statement.