Introduction to a T test
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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
This solution provides the statistics on an evolutionary theory.
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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 ...
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- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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