a random sample of 100 students from the current years batch gives the mean IQ level of 110 and variance of 5 can we say that this is same as the IQ of the previous batch which was 116.

Question

a random sample of 100 students from the current years batch gives the mean IQ level of 110 and variance of 5 can we say that this is same as the IQ of the previous batch which was 116.

Answer 1

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

Variance = SD^2

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score. Depending on the level of significance you are using, P = .05 or P = .01. If proportion is larger than the one you are using, we would say it is essentially the same.