IQ scores for the general population form a normal distribution with a population mean of 100 and a population standard deviation of 15. However, there are data that indicate that children’s intelligence can be affected if their mothers have German measles during pregnancy. Using hospital records, a researcher obtained a sample of 20 school children whose mothers all had German measles during their pregnancies. The average IQ for this sample was 97.3. 

a. State the null and alternative hypotheses for this scenario in words and in symbols. 

b. Use the z-score test to determine if the sample mean is significantly different from the population mean (show all work) 

c. Would you accept or reject the null hypothesis? State your conclusion about the intelligence of children whose mothers had German measles during pregnancy.