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Chapter 13: Problem 27

A mother wants to predict the height of her full-grown son on the basis of his height at the age of 8 years. Should she use a prediction interval or a confidence interval? Why?

Short Answer

Expert verified
The mother should use a prediction interval as it provides a range in which her individual son's height is likely to fall.

Step by step solution

01

Recognizing the problem type

The mother is not trying to predict a range for all 8-year-olds or the average height of an 8-year-old who grows to a certain height but instead, she wants to predict her son's specific future height. This is an individual prediction.
02

Deciding on the appropriate statistical measure

For individual level predictions like this, prediction intervals are normally the appropriate choice. While a confidence interval could help estimate the average height of full-grown individuals given their height at the age of 8, this doesn't really help in the mother's specific requirement.
03

Providing justification

A prediction interval, on the other hand, accounts for additional uncertainty involved in predicting a specific value as opposed to average tendencies. Therefore, this would be the recommended type of interval to use.

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Most popular questions from this chapter

Excessive lead levels can negatively affect brain functions; lead poisoning is particularly dangerous to children. A study was conducted to find out whether children of battery factory workers had higher levels of lead in their blood than a matched group of children. Each child in the experimental group was matched with a child in the control group of the same age, living in the same neighborhood. Although these children were not a random sample, we can test the hypothesis that the difference is too large to occur by chance if the child from the control group was randomly chosen. The figure shows a histogram of the differences in lead level. The differences were found by calculating "factory child's lead level minus matched control child's lead level." Lead levels were concentrations in the blood, measured in micrograms per deciliter. A positive difference means the child of a factory worker has a higher lead concentration than the child in the control group. The data consisted of 1 tie (the same value for the child and the matching child), 28 pairs in which the factory worker's child had a higher level, and 4 pairs in which the factory worker's child had a lower level of lead. Carry out a sign test to determine whether children whose parents are exposed to lead at work have a higher lead level than children whose parents are not exposed to lead at work. Use a significance level of \(0.05\) to see whether the experimental group had higher levels of lead. (These data appear in Trumbo [2001].)

Suppose a college career center was interested in the starting salaries of recent graduates in Communications Studies and Sociology. The center randomly samples 15 recent graduates from each of these fields and records the starting salary for the graduates. The center wants to determine whether there is a difference in the starting salaries for graduates in these majors. Which test(s) should be used in each of these situations? a. Assume the starting salary for both majors is approximately Normally distributed. b. Assume that one of the salary distributions is strongly right-skewed.

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Suppose you want to determine whether meditation can cause a decrease in pulse rate. You randomly select 15 students, teach them a meditation technique, and then measure their pulse rates before and after meditation. Which test(s) should you choose for each situation? a. Assume that your analysis shows that the differences in pulse rates are Normally distributed. b. Assume that the distributions of differences in pulse rates are strongly skewed.

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