Module 6 - One-sample testing - Sample size n=9 Population...

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A new species of bacterium is discovered and a researcher measures reproduction time to investigate the rate of reproduction in this new species. Mean reproduction time across all other bacteria species is 120 minutes . Pair/Share: (1) Rank (A-D) the data distributions (i.e., samples) in terms of the evidence they appear to provide that this new bacterium reproduces at a mean rate that is different from the mean for all other bacteria. (2) What characteristics of each sample influence your decisions? A B C D Sample size: n=9 Population Parameters: μ =105, σ =10 Sample size: n=9 Population Parameters: μ =105, σ =20 Sample size: n=40 Population Parameters: μ =105, σ =10 Sample size: n=40 Population Parameters: μ =105, σ =20
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I. One-sample t-test A. Purpose of use 1. A one-sample t-test determines the probability that a sample of ratio-interval scale data was taken from a population with a pre- determined mean 2. The pre-determined mean is an a priori constant value Module 6 – One-Sample Testing
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C. Null and alternative hypotheses 1. Null hypothesis H 0 : μ = c In words: The mean of the population ( μ ) from which the sample came is equal to (not different than) the constant value (c) 2. Alternative hypothesis H A : μ ≠ c In words: The mean of the population ( μ ) from which the sample came is not equal to (is different than) the constant value (c) Note this type of test is used when you have a question of “difference” (not a question of “relationship”)
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D. Test statistic 1. The test statistic calculated to determine the probability that the sample came from a population in which the null hypothesis is true (the mean of the population equals the a priori constant value) is t 2. Equation for t E. Degrees of freedom (n-1)
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H 0 : μ = c H A : μ ≠ c Pair/Share: Why are different symbols used for the mean in the hypotheses and the test statistics equation? What do the two parts of the symbol for sample standard error represent? “We use sample statistics to estimate population parameters.” μ = (“mu”) population mean 𝑋𝑋 = (“x bar”) sample mean σ = (“sigma”) population standard deviation s = (“s”) sample standard deviation
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F. When dealing with one-sample (and two-sample) tests, you must make the distinction between one-tailed and two-tailed tests 1. Two-tailed tests: a. Used when there is NO a priori expectation as to the direction
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