Answered: A random sample of 49 measurements from one population had a sample mean of 16, with sample standard deviation 5. An independent random sample of 64…

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Description: A random sample of 49 measurements from one population had a sample mean of 16, with sample standard deviation 5. An independent random sample of 64 measurements from a second population had a sample mean of 19, with sample standard deviation 6. Test

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Question

A random sample of 49 measurements from one population had a sample mean of 16, with sample standard deviation 5. An independent random sample of 64 measurements from a second population had a sample mean of 19, with sample standard deviation 6. Test the claim that the population means are different. Use level of significance 0.01.

I need help with Compute the corresponding sample distribution value. (Test the difference ?₁ − ?₂. Round your answer to three decimal places.)

(a) What distribution does the sample test statistic follow? Explain.
O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
O The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
(b) State the hypotheses.
O Ho: H1 = H2i H1: H1 < M2
O Ho: H1 = H2i Hz: H1 # H2
O Ho: H1 # H2i H: H1 = H2
O Ho: H1 = H2i Hz: µ1 > H2
(c) Compute x, - x2.
x1 - x, =
Compute the corresponding sample distribution value. (Test the difference u, - H2: 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) Conclude the test.
O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
(f) Interpret the results.
O Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.
Reject the null hypothesis, there is insufficient evidence that there is a difference between the population means.
O Reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.
O Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means.

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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