Below are the SPSS results of a related (dependent) samples t-test. Use the SPSS results to answer Questions 5, 6, and 7.Paired Samples Statistics MeanNStd. DeviationStd. Error MeanPair 1Statistics Posttest57.12504016.739622.64677Statistics Pretest49.92504015.090142.38596 Paired Samples Test Paired DifferencestdfSig.(2-tailed) MeanStd. DeviationStd. Error Mean Pair 1Statistics Posttest - Statistics Pretest7.20012.313( a )( b )( c ).001 Find the mean of the differences ( and standard deviation of the differences (Sd). Replace “a,” “b,” and “c” in the table above with the correct values. Round to the third decimal place.Do you think there is a statistically significant difference between the pretest and posttest at the .05 level of significance?

Let xi; (i=1,2,...,n)and yi; (i=1,2,...,n) are two samples of same sizes and these two samples are…

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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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Below are the SPSS results of a related (dependent) samples t-test. Use the SPSS results to answer Questions 5, 6, and 7.

Paired Samples Statistics
	Mean	N	Std. Deviation	Std. Error Mean
Pair 1	Statistics Posttest	57.1250	40	16.73962	2.64677
Statistics Pretest	49.9250	40	15.09014	2.38596

Paired Samples Test
	Paired Differences	t	df	Sig. (2-tailed)
Mean	Std. Deviation	Std. Error Mean

Pair 1	Statistics Posttest - Statistics Pretest	7.200	12.313	( a )	( b )	( c )	.001

Find the mean of the differences ( and standard deviation of the differences (S_d).

Replace “a,” “b,” and “c” in the table above with the correct values. Round to the third decimal place.

Do you think there is a statistically significant difference between the pretest and posttest at the .05 level of significance?

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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