For a random sample of 36 data pairs, the sample mean of the differences was 0.77. The sample standard deviation of the differences was 2. At the 5% level of significance, test the claim that the population mean of the differences is different from 0. (a) Is it appropriate to use a Student's t distribution for the sample test statistic? Explain.O Yes, the sample size is larger than 30.O No, the standard deviation is not smaller than the sample mean.O Yes, the standard deviation is larger than the sample mean.O No, the sample size is not larger than 30.What degrees of freedom are used?(b) State the hypotheses.O Ho: Ha = 0; H,: H# 0O Ho: Hd = 0; H1: Hd>0O Ho: Hd = 0; H4: Hd <0O Ho: Hg# 0; Hq: Hd = 0(c) Compute the t value. (Round your answer to three decimal places.)(d) Estimate the P-value of the sample test statistic.O P-value > 0.500O 0.250 < P-value < 0.500O 0.100 < P-value < 0.250O 0.050 < P-value < 0.100O 0.010 < P-value < 0.050O p-value < 0.010(e) Do we reject or fail to reject the null hypothesis? Explain.O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.(f) What do your results tell you?O Fail to reject the null hypothesis, there is sufficient evidence to conclude that the population mean of the differences is not zero.O Reject the null hypothesis, there is sufficient evidence to conclude that the population mean of the differences is not zero.O Fail to reject the null hypothesis, there is insufficient evidence to conclude that the population mean of the differences is not zero.O Reject the null hypothesis, there is insufficient evidence to conclude that the population mean of the differences is not zero.

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Description: For a random sample of 36 data pairs, the sample mean of the differences was 0.77. The sample standard deviation of the differences was 2. At the 5% level of significance, test the claim that the population mean of the differences is different from 0

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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

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For a random sample of 36 data pairs, the sample mean of the differences was 0.77. The sample standard deviation of the differences was 2. At the 5% level of significance, test the claim that the population mean of the differences is different from 0.

(a) Is it appropriate to use a Student's t distribution for the sample test statistic? Explain.
O Yes, the sample size is larger than 30.
O No, the standard deviation is not smaller than the sample mean.
O Yes, the standard deviation is larger than the sample mean.
O No, the sample size is not larger than 30.
What degrees of freedom are used?
(b) State the hypotheses.
O Ho: Ha = 0; H,: H# 0
O Ho: Hd = 0; H1: Hd>0
O Ho: Hd = 0; H4: Hd <0
O Ho: Hg# 0; Hq: Hd = 0
(c) Compute the t value. (Round your answer to three decimal places.)
(d) Estimate the P-value of the sample test statistic.
O P-value > 0.500
O 0.250 < P-value < 0.500
O 0.100 < P-value < 0.250
O 0.050 < P-value < 0.100
O 0.010 < P-value < 0.050
O p-value < 0.010
(e) Do we reject or fail to reject the null hypothesis? Explain.
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(f) What do your results tell you?
O Fail to reject the null hypothesis, there is sufficient evidence to conclude that the population mean of the differences is not zero.
O Reject the null hypothesis, there is sufficient evidence to conclude that the population mean of the differences is not zero.
O Fail to reject the null hypothesis, there is insufficient evidence to conclude that the population mean of the differences is not zero.
O Reject the null hypothesis, there is insufficient evidence to conclude that the population mean of the differences is not zero.

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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