Answered: Test the claim that the treatment…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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1) Test the claim that the treatment population has a smaller mean than the placebo population, using the α=0.01 significance level and assuming that the populations are normally distributed. Set things up in terms of (treatment group)-(placebo group). Treatment group: n=5, x=69, s=5.6. Placebo group: n=10, x=78, s=5.3. (a) The test statistic is (give at least three digits after the decimal point). (b) What is the conservative estimate for the degrees of freedom? df = (c) The P-value is (give at least three digits after the decimal point). (e) Is there sufficient evidence to warrant the rejection of the claim that the treatment and placebo populations have the same mean?

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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