Each student in a class was classified according to the scale: 17 - 20 years Cat
ID: 3183254 • Letter: E
Question
Each student in a class was classified according to the scale: 17 - 20 years Category 1; 21 - 24 years Category 2; 25 years & above Category 3.
The distribution of their final grade in Statistics according to the Age classification was developed and processed using MINITAB and the following output was obtained: MTB > ChiSquare ‘Grade A’ ‘Grade B’ ‘Grade C’ ‘Grade D’ ‘Grade E’ .
Chi-Square Test for Association: Grade, Age
Rows: Age Columns: Grade
Cell Contents: Count
Expected count
Contribution to Chi-square
Chi-Square = 11.333, DF = 8, P-Value = 0.1835
WARNING * 5 cells with expected counts less than 5.0
(a) State the null and alternative hypotheses for this investigation>
(b) Calculate the missing values marked *, ** and ***.
(c) State clearly any assumptions made in calculating the values in Part (b).
(d) Comment on the warning statement to the end of the output.
(e) Explain how you would adjust the output so as to eliminate the warning.
(f) State a conclusion from this investigation.
A B C D E All 1 7 13 17 16 18 71 8.61 13.98 * 13.98 14.52 0.300 0.069 0.423 0.290 0.833 2 6 11 19 9 9 *** 6.55 10.64 15.14 10.64 11.05 0.045 0.012 *** 0.252 0.379 3 3 2 1 1 0 7 0.85 1.38 1.96 1.38 1.43 5.456 0.280 0.472 0.104 1.432 All 16 26 37 26 27 132Explanation / Answer
a) H0 Null: Age category and Grade are independent
H1alternate: age category and Grade are not independent
b) * - 71*37/132 = 19.9
*** - the total
71+x+7 = 132.
x = 54
chi square contribution ***
(Orc - Erc)2 / Erc
= (19-15.14)2 / 15.14 = 0.984
C)
D) more than 20% of the contingency cells are having expected values < 5. It should be greater than that to ensure smooth chi square test.
E) Reduce the age range in the second category so that those frequencies move to the third category. E.g make the second age category as 21-23
F) p-value > 0.05, hence donot reject H0 null hypothesis. Conclude that age category and grade are independent
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