Question

The mean I.Q of a sample of 1600 children was 99. It is likely that this was a random sample from a population with mean I.Q 100 and standard deviation 15.

 Required:

Using appropriate statistics, deduce whether there is any statistically significant difference between the two means if z critical value at α = .05 is 1.96        

Answer 1

Given, n=1600

mean $\mu=100$

Standard deviation $\sigma=15$

Average weight X=$99$

Z-score=$\dfrac{x-\mu}{\sigma}$

$=\dfrac{99-100}{15}=|\dfrac{-1}{15}|=0.066$

Since The calculated value of z is less thn the critical value 1.96,

So There is no significant difference between the two means.