Answer to Question #120467 in Statistics and Probability for Joseph Se

Question

Researchers studying IQ scores of 36 gifted children and their parents. First, differences in IQ scores were calculated as father's IQ score - mother's IQ score. The dot plot below shows the bootstrap distribution of means of 200 bootstrap samples taken from this original sample of differences in IQ scores. The mean of the bootstrap distribution is approximately -3.48 points and the bootstrap standard error is 1.3 points. Which of the following statements is false?

A. Since 0 is apparently an unusual value for the statistic, then at the 5% significance level we would fail to reject a null hypothesis of that claims that the fathers' and mothers' average IQs are equal.
B. A 95% bootstrap confidence interval for the difference in IQ scores is approximately (-6, -0.9).
C. It's likely that in the original sample, most mothers had higher IQ scores than the fathers.
D. A 90% bootstrap confidence interval for the difference in IQ scores would is approximately (-5.6, -1.3).

Answer 1

$\text{A is the false statement because}\\ Z=\frac{-3.48}{1.3}=-2.68\\ the\; rejection\, region\; is\; Z<-1.96, Z>1.96\\ The\; decision\; is\; to\; reject\; H_{0}$