6 boys are selected at random from a school their marks in mathematics are found to be 66,63,63,64,60,68 out of 100. in the light of this marks, discuss the general observations that the mean marks in mathematics in the school were 66.
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Given :- 6 boys are selected at random from a school their marks in mathematics are found to be 66,63,63,64,60,68 out of 100. in the light of this marks, discuss the general observations that the mean marks in mathematics in the school were 66.
Solution :-
given that,
→ Total number of students of a school selected = 6 boys
and,
→ Total marks of these students in mathematics = 66 + 63 + 63 + 64 + 60 + 68 = 384
then,
→ Mean marks in mathematics = Total marks / Total number of students = 384/6 = 64
now,
→ sum of all (mean - marks)² = (64 - 66)² + (64 - 63)² + (64 - 63)² + (64 - 64)² + (64 - 60)² + (64 - 68)² = (-2)² + 1² + 1² + 0² + 4² + (-4)² = 4 + 1 + 1 + 16 + 16 = 38
then,
→ standard deviation = √(sum of all (mean - marks)² / (n - 1) = √(38/5) ≈ 2.76
given that,
→ mean marks were = 66
now,
→ T statistics = | Actual mean - given mean | / standard deviation * √n
→ T statistics = {|64 - 66| / 2.76} * √6 ≈ 1.78
now, checking critical value from table we get,
→ n = 6
so,
→ degree of freedom = 6 - 1 = 5
then,
→ critical value of t at 5% significant level from the table is = 2.57
as we can see that,
→ 2.57 > 1.78
→ critical value > T statistics .
therefore, we can conclude that, given mean marks were accepted .
Hence, the mean marks in mathematics in the school were 66.
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