Question

The mean I.Q of a sample of 1600 children was 99. Is it likely that this was a random sample from a population with mean I.Q 100 and standard deviation 15? (Test at 5% level of significance)

Answer 1

n (Sample size) = 1600 children 

\(\overline{x}\) (Sample mean) = 99 

µ (Population mean) = 100 

σ (Population SD) = 15 

α (Level of significance) = 5% 

Null hypothesis H₀ : µ = 100

(Sample has been drawn from a population with mean 100 and S.D 15) 

Alternative hypothesis H₁ : µ ≠ 100

(Sample has not been taken from a population with mean 100 and S.D 15) 

Test statistic :

The significant value or table value Z_α/2= 1.96. 

Comparing the values, we see that 2.67 > 1.96 (or) Z > Z_α/2  at 5% level of significance. So the null hypothesis is rejected. Hence we conclude that the random sample is not taken from a population with mean I.Q = 100 and S.D = 15.