6.5 Gifted children. Researchers collected a simple random sample of 36 children who had been identied as gifted in a large city. The following histograms show the distributions of the IQ scores of mothers and fathers of these children. Also provided are some sample statistics.\" 12 12 12 8 8 8 4 4 4 0 O 0 100 120 140 110 120 130 Mother's IQ Faiher's IQ Mother Father Di'. Mean 118.2 114.8 3.4 SD 6.5 3.5 7.5 n 36 36 36 (a) Are the IQs of mothers and the IQs of fathers in this data set related? Explain. (b) Conduct a hypothesis test to evaluate if the scores are equal on average. Make sure to clearly state your hypotheses, check the relevant conditions, and state your conclusion in the context of the data