A random sample of n = 4 individuals is selected from a population with µ = 35, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 40.1 with SS = 48. Use the Distributions tool to help answer the questions that follow. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.) If there is no treatment effect, how much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.) Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with α = .05. (Show three decimal places.) t-critical = ± t = The results indicate: Failure to reject the null hypothesis; there is not a significant treatment effect. Failure to reject the null hypothesis; there is a significant treatment effect. Rejection of the null hypothesis; there is not a significant treatment effect. Rejection of the null hypothesis; there is a significant treatment effect.

Ciccarelli: Psychology_5 (5th Edition)

5th Edition

ISBN:9780134477961

Author:Saundra K. Ciccarelli, J. Noland White

Publisher:Saundra K. Ciccarelli, J. Noland White

Chapter1: The Science Of Psychology

Section: Chapter Questions

Problem 1TY

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Question

A random sample of n = 4 individuals is selected from a population with µ = 35, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 40.1 with SS = 48. Use the Distributions tool to help answer the questions that follow.

How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.)

If there is no treatment effect, how much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.)

Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with α = .05. (Show three decimal places.)