In a study of parents' perceptions of their children's size, researchers Kaufman et al. (Current Biology, 2013) asked parents to estimate their youngest child's height. The researchers hypothesized that parents tend to underestimate their youngest child's size because the youngest child is the baby of the family and everybody else is the family appears bigger compared to the baby. The sample of 3434parents who were surveyed underestimated their youngest child's height by 7.47.4cm, on average; the standard deviation for the difference in actual heights and estimated heights was 7.057.05cm and the data are not strongly skewed.

Is there evidence that youngest children's heights tend to be underestimated by their parents? Carry out a theory-based test using an appropriate applet or statistical software. Find and report a p-value as well as a standardized statistic.Round the test statistic to 2 decimal places, e.g. 5.83, and the p-value to 4 decimal places, e.g. 0.0583. t = Enter you answer; t , p-value = Enter you answer; p-value

Interpret the p-value in the context of the study.

a. We obtain values of 7.4 cm or larger by chance less than 0.0001 of the time if parents are estimating the mean heights of the children inaccurately.

b. We obtain values of 7.4 cm or larger by chance less than 0.0001 of the time if parents are estimating the heights of the children inaccurately on average from a population.

c. We obtain values of 7.4 cm or larger by chance less than 0.0001 of the time if parents are estimating the heights of the children accurately on average from a sample.

d. We obtain values of 7.4 cm or larger by chance less than 0.0001 of the time if parents, in the long run, are estimating the heights of the children accurately.

Using an appropriate applet or statistical software, find a 95% confidence interval for the difference.Round your answers to 2 decimal places, e.g. 5.83. Confidence interval = (Enter your answer; confidence interval, lower bound , Enter your answer; confidence interval, upper bound )