A random sample (n=16) is obtained from a population with a mean of 70, and a treatment is administered. After treatment, the sample mean is found to be M = 75 and the sample variance is 81. Conduct a one-sample t test (alpha = .05, two-tailed). a) State the null and alternative hypotheses in SYMBOLS only. Null: Alternative: b) What is the critical t? c) What is the observed t-statistic? d) Are there significant differences between the sample and the population? (yesor no) e) Should we reject the null or fail to reject the null? f) Calculate variance explained (r2):

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Description: A random sample (n=16) is obtained from a population with a mean of 70, and a treatment is administered. After treatment, the sample mean is found to be M = 75 and the sample variance is 81. Conduct a one-sample t test (alpha = .05, two-tailed). a

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A random sample (n=16) is obtained from a population with a mean of 70, and a treatment is administered. After treatment, the sample mean is found to be M = 75 and the sample variance is 81. Conduct a one-sample t test (alpha = .05, two-tailed).

a) State the null and alternative hypotheses in SYMBOLS only.

Null:

Alternative:

b) What is the critical t?

c) What is the observed t-statistic?

d) Are there significant differences between the sample and the population? (yesor no)

e) Should we reject the null or fail to reject the null?

f) Calculate variance explained (r2):

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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