To evaluate the effect of a treatment, a sample of n = 8 is obtained from a population with a mean of μ = 50, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 55.Assuming that the sample variance is s^2 = 32 , use a two-tailed hypothesis test with α = .05 to determine whether the treatment effect is significant and compute both Cohen’s d and r^2 to measure effect size.Assuming that the sample variance is s^2 = 72 , repeat the test and compute both measures of effect size.Comparing your answers for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test and measures of effect size?

Name: To evaluate the effect of a treatment, a sample of n = 8 is obtained
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Description: To evaluate the effect of a treatment, a sample of n = 8 is obtained from a population with a mean of μ = 50, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 55.Assuming that th

1. The null and alternative hypothesis are given by : Ho : μ=50H1 : μ≠50 The test statistics is given by Students' t-distribution : t=x-μs2/n~tn-1 t=55-5032/8=2.5 The degrees of freedom are (8-1)=7 The two-tailed critical t-value at α=0.05, df=7 is ±2.365 The decision rule states : Null hypothesis is rejected when calculated test statistics is greater than the tabulated t-value and is accepted other wise. Since the calculate value 2.5 is greater than tabulated value 2.365, the null hypothesis is rejected concluding that the treatment does not have any significant effect. Cohen's d formula is given by : d=x-μs=55-5032=0.88 The Cohen's d-value indicates a large effect. The formula for R2 is given by : R2=t2t2+df=2.522.52+7=0.472 2. For sample variance s2=72, the test statistics and the measure of effect sizes are : t=55-5072/8=1.67 For the same critical value, the null hypothesis this time is accepted because the calculated test statistics 1.76 is less than the tabulated value 2.365, concluding that the population mean is not equal to 50. Cohen's d and r2 in this case are : d=55-5072=0.589 There is a medium effect. r2=1.6721.672+7=0.285 3. The increase in the variability of the scores decreases the test statistics, the Cohen's d and the R2

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To evaluate the effect of a treatment, a sample of n = 8 is obtained from a population with a mean of μ = 50, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 55.

Assuming that the sample variance is s^2 = 32 , use a two-tailed hypothesis test with α = .05 to determine whether the treatment effect is significant and compute both Cohen’s d and r^2 to measure effect size.
Assuming that the sample variance is s^2 = 72 , repeat the test and compute both measures of effect size.
Comparing your answers for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test and measures of effect size?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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