Question

For example, researchers were trying to determine if drug XXX, administered during infancy, resulted in cognitive impairments. They identified 10 children who had taken drug XXX as infants and tested the IQ score for these children. The average IQ score for these children was 90.8. They compared that to the national average, which is 100 (with a standard deviation of 15). Based on these numbers, they calculated a z statistic of - 1.94. (See calculation below.) This calculated value of z does not exceed the critical value of z at the .05 level of significance (±1.96), so the researchers cannot reject the null hypothesis; the difference is not statistically significant.

1. Explain why researchers who find that a difference is not statistically significant cannot assume that no difference exists.

2. Does this prove that drug XXX is safe?  

3.Since the difference was not found to be statistically significant, can we conclude that children that were treated with drug XXX were no different in measured intelligence than those who were not exposed to drug XXX? Why or why not?

Answer 1

Sinc ethe given information provide us that the sample Size =10

Population mean( ) = 100 IQ

Population SD = 15 IQ

Sample mean ()= 90.8

At 5% level of significance. The the crtical value of z = +-1.96

This value is considered as the threshold point for the null hypothesis to be accepted.

NUll Hypothesis (H0) :

Alternate Hypothesis (Ha) :

To reject the Null hypothesis, CAlculated Z should be greater than 1.96 or less than -1.96

And If calculated value of Z lying between +1.96 and -1.96 Then the null hypothesis is accepted.

1. Since the calculated z = -1.94

That lies between  +1.96 and -1.96. Thus reseacher can not assume that there is a significant difference.

2. Since there is no significant difference in the sample mean and the population means even after drug accumulation. Thus , we can conclude that the drug XXX is SAFE fo use.

3. If the value of calculated z was more than +1.96 then we can say that the drug was positively effective and if the value of calculated z was less than -1.96 then we can say that the drug was negatively effective and had adverse effect on the subjects.

Since there is no significant difference between the sample mean and the population mean thus we can conclude that the children who were treated with the drug has no significant difference in the intelligence measured.