Given the scenario: IQ scores from the general population form a normal distribu

Question

Given the scenario: IQ scores from the general population form a normal distribution with a m = 100 and s = 15. However, data indicate that children’s intelligence may be affected if their mothers have German measles during pregnancy. Using hospital records, a researcher obtained a sample of n = 64 school children whose mothers all had German measles during their pregnancies. The average IQ for this sample was x = 94. Do these data indicate that German measles have a significant effect on IQ? Test with P=0.05.

Note

µ = population mean

x = sample mean

s = standard deviation

What is the level of significance to be used?

What is your decision rule? (In other words, what is your rejection region?)

Calculate the z statistic

Do you reject or fail to reject the null hypothesis?

Is a child’s intelligence affected if the mother has German measles during pregnancy?

Explanation / Answer

1)level of significance to be used =0.05

for 0.05 level ; critical z=1.96

2)therefore rejectio region : if test stat z>1.96 or z<-1.96 ; reject null hypothesis

3) for n=64; std error of mean =std deviation/(n)1/2 =15/(64)1/2 =1.875

therefore test stat z=(X-mean)/std error =(94-100)/1.875=-3.2

as test stat z falls into critical region; we reject null hypothesis.

therefore we have sufficient evidence to conclude that a child’s intelligence affected if the mother has German measles during pregnancy

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