Question

Suppose you start up a company that has the developed a drug that is supposed to increase IQ.   You know that the standard deviation of IQ in the general population is 45. You test your drugs on 36 patients and obtain I mean IQ of 103. Using a alpha value of 0.05, is this IQ significantly different from the population mean of 100?

Answer 1

Population standard deviation is known, so we will use z distribution for calculation.

It is given that population standard deviation = 45

population mean and sample mean = 103

sample size n = 36

We have to test the statement whether the IQ significantly different from 100

So,

Formula for z statistics is given as

setting the given values, we get

Using z distribution table for two tailed hypothesis, we get critical rejection region -1.96 and +1.96

So, any value within -1.96 and 1.96 will be considered insignificant and null hypothesis will be retained within this range.

Any value outside -1.96 and +1.96 range will be considered significant and null hypothesis will be rejected.

In this, z calculated value is 0.4, which is inside the -1.96 and +1.96 region, so we will not reject the null hypothesis

We can conclude that the result is not significant and the IQ is not significantly different from the population mean of 100