A state educational committee collected the following data in one county to see if age group and educational level are related.The counts in thousands are in the table.

Do the data show that educational attainment and age are independent?Test at the 5% level.

Education. Age Group Row Total

25-34 35-44 45-54 55-64 >64

Did not complete HS 54 50 57 76 33 270

Competed HS 64 85 44 80 75 348

College 1-3 years 60 55 31 25 25 196

College 4 or more years 47 45 39 31 24 186

Column Total 225 235 171 212 157 1000

This is another Chi-Square test for independence.

All given 20 numbers are Observed values ( O ).Write them downin one column.

O E O - E (O - E)² (O - E)²/E

54

64

60

47

50

85

55

45

57

44

31

39

76

80

25

31

33

75

25

24

Complete the E-column

Complete the rest of the table

Chi-Squarec will bethe total of the last column

Use online Chi-Square calculator:https://www.socscistatistics.com/pvalues/chidistribution.aspx

and find p-value.Degree of Freedom for given data is(4-1)(5-1) = 12.

Compare p-value toa= 0.05 and make the conclusion.