# T test for population mean

Evolutionary theories often emphases that humans have adapted to their physical environment. One such theory hypothesizes that people should spontaneously follow a 24-hour cycle of sleeping and waking - even if they are not exposed to the usual pattern of sunlight. To test this notion, eight paid volunteers were placed (individually) in a room in which there was no light from the outside and no clocks or other indications of time. They could turn the lights on and off as they wished. After a month in the room, each individual tended to develop a steady cycle. Their cycles at the end of the study were as follows: 25, 27, 25, 23, 24, 25, 26, and 25.

In this problem, you will reach a conclusion about the theory that 24 hours is the natural cycle (that is, does the average cycle lengths under these conditions differ significantly from 24 hours?) Before figuring your response, you must decide what hypothesis test you will use (for example, single sample t-test, dependent samples t-test, independent samples t-test, ANOVA, etc.) Then, using the 5% level of significance, determine the following:

a. The null and research hypothesis

b. The comparison distribution used (for example, a t-distribution of 20 degrees of freedom , a t-distribution of 32 degrees of freedom, etc.)

c. The cutoff score on the comparison distribution (for example, a t-critical or "cutoff t" of 1.5 etc.)

d. Your sample's test score (for example, a t-score of 2.4)

e. Your conclusion on whether to accept or reject the null hypothesis (you must show how the comparison of your cutoff score with your sample's test score leads to your conclusion.)

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#### Solution Summary

The solution provides step by step method for the calculation of test statistic for t distribution . Formula for the calculation and Interpretations of the results are also included.