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
n1 = 49
measurements from a population with population standard deviation
?1 = 3
had a sample mean of
x1 = 9.
An independent random sample of
n2 = 64
measurements from a second population with population standard deviation
?2 = 4
had a sample mean of
x2 = 11.
Test the claim that the population means are different. Use level of significance 0.01.
(a) Check Requirements: What distribution does the sample test statistic follow? Explain.
(b) State the hypotheses.
(c) Compute
Compute the corresponding sample distribution value. (Test the difference ?1 − ?2. Round your answer to two decimal places.)
(d) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)
(e) Conclude the test.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.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.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
(b) State the hypotheses.
H0: ?1 = ?2; H1: ?1 < ?2H0: ?1 = ?2; H1: ?1 > ?2 H0: ?1 = ?2; H1: ?1 ≠ ?2H0: ?1 ≠ ?2; H1: ?1 = ?2
(c) Compute
x1 − x2.
x1 − x2 =
Compute the corresponding sample distribution value. (Test the difference ?1 − ?2. Round your answer to two decimal places.)
(d) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)
(e) Conclude the test.
At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
(f) Interpret the results.Fail to reject the null hypothesis, there is insufficient 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. Reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.
Expert Solution
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Step 1
Given Data :
For Sample 1
x̄1 = 9
σ1 = 3
n1 = 49
For Sample 2
x̄2 = 11
σ2 = 4
n2 = 64
Significance level, α= 0.01
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