A Swimming School Claimed That the Average Seven-Year-Old Would Be

question 19

Essay

A swimming school claimed that the average seven-year-old would be able to swim across an Olympic-sized pool in less than 2 minutes after taking lessons from their instructors.To test this claim,a consumer psychologist arranged for eight randomly selected seven-year-old children to take lessons at the school and recorded how long it took each child to swim across a pool at the end of the lessons.The times (in seconds)were 60,120,110,80,70,90,100,and 130.What conclusion would the psychologist draw following a t test for a single sample using 120 seconds as the "known" population mean and the .05 significance level?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Explain the logic of what you did to a person who is familiar with hypothesis testing with a known population variance and a single sample,but who knows nothing about t tests of any kind (for example,you do not need to describe the steps or logic of hypothesis testing).Be sure you explain how this problem differs from a problem with a known population variance and a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and all the figuring you did to determine those characteristics.

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Definitions:

Mixed Feelings

Having contradictory emotions about something at the same time, such as happiness and sadness.

Personal Growth

The process of enhancing self-awareness, knowledge, skills, and overall well-being.

Interpretation

The process of explaining, reframing, or providing meaning to a particular piece of information, event, or work of art.

Psychoanalyst

A professional who practices psychoanalysis, a therapeutic approach developed by Freud that explores unconscious conflicts and desires influencing behavior.