Question: For each of the following situations, state whether the distribution of interest is a z distribution, a t distribution, or an F distribution. Explain your answer.

1. A student reads in her Introduction to Psychology textbook that the mean IQ is 100. She asks 10 friends what their IQ scores are (they attend a university that assesses everyone’s IQ score) to determine whether her friends are smarter than average.
2. Is the presence of books in the home a marker of a stable family? A social worker counted the number of books on view in the living rooms of all the families he visited over the course of one year. He categorized families into four groups: no books visible, only children’s books visible, only adult books visible, and both children’s and adult books visible. The department for which he worked had stability ratings for each family based on a number of measures. This is an F statistic, because the independent variable is a categorical variable.
3. Which television show leads to more learning? A researcher assessed the vocabularies of a sample of children randomly assigned to watch Sesame Street as much as they wanted for a year but not to watch The Wiggles. She also assessed the vocabularies of a sample of children randomly assigned to watch Wiggles as much as they wanted for a year but not to watch Sesame Street. She compared the average vocabulary scores for the two groups

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