A researcher conducts a study on the size of a cancerous tumor on the same patient before and after receiving a new treatment. Test that the mean differences in tumor sizes significantly decreases after therapy at a significance level of 0.01. SubjectBeforeAfter15.35.024.44.034.94.546.46.0What is/are the critical values, What is D bar, standard deviation, observed test statistic ? If the correct answer has a positive and negative value, enter only the positive value.

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Description: A researcher conducts a study on the size of a cancerous tumor on the same patient before and after receiving a new treatment. Test that the mean differences in tumor sizes significantly decreases after therapy at a significance level of 0.01. Subjec

Given the data- Subject Before After Difference(d) 1 5.3 5.0 0.3 2 4.4 4.0 0.4 3 4.9 4.5 0.4 4 6.4 6.0 0.4 Total 21 19.5 1.5 Here; n=4d¯=0.375 Pooled standard deviation is given by- SDpooled=(SD12+SD22)2 where SD1=0.85049SD2=0.85391 Hence pooled SD is given as- SDpooled=SD12+SD222=0.850492+0.8539122=0.8522 Null and alternate hypothesis is- H0:mean difference between paired observations is zero(μd=0).Ha:mean difference between paired observations is not zero(μd≠0). Test statistic is calculated as- t=d¯(SDn) Substituting all the values in the test statistic, we get; t=0.3750.85224=0.3750.4261=0.88 Critical t value at 3 degree of freedom at 0.01 significance level is 5.841. Calculated t value is less than the tabulated t value, hence we will reject the null hypothesis and conclude that there is enough evidence to claim that the mean difference in tumor sizes significantly decreases after the therapy.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A researcher conducts a study on the size of a cancerous tumor on the same patient before and after receiving a new treatment. Test that the mean differences in tumor sizes significantly decreases after therapy at a significance level of 0.01.

Subject	Before	After
1	5.3	5.0
2	4.4	4.0
3	4.9	4.5
4	6.4	6.0

What is/are the critical values, What is D bar, standard deviation, observed test statistic ? If the correct answer has a positive and negative value, enter only the positive value.

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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