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2. Research groups A and B have studied independently a phenomenon that can be described by random sampling from a normal distribution N(μ, σ²), where both parameters are unknown. The interesting parameter is is the population average μ. Results of research groups (sample size, sample mean and sample variance) are respectively nA = 10, NB = 15, A = 3.967, s B = 3.522, s = 1.995, = 1.310. We would like to do meta analysis, i.e. combine the research results of these two groups. We set the hypotheses H₁: µ = 3 and H₁: µ 3. Hypotheses are tested using a two-sided t-test and significance level 0.05. (a) Calculate the usual point estimater for the parameters μ and σ² by using the data sets of both group A and group B. (First determine nA+B, A+B and s² A+B using the given information¹ on the data sets.) (b) Test the hypotheses using the data of the group A (α = 0.05). State the p-value of the test and the decision of rejecting or accepting the null hypothesis. (c) Test the hypothesis using the meta data of groups A and B (α = 0.05).

2. Research groups A and B have studied independently a phenomenon that can be described by random sampling from a normal distribution N(μ, σ²), where both parameters are unknown. The interesting parameter is is the population average μ. Results of research groups (sample size, sample mean and sample variance) are respectively nA = 10, NB = 15, A = 3.967, s B = 3.522, s = 1.995, = 1.310. We would like to do meta analysis, i.e. combine the research results of these two groups. We set the hypotheses H₁: µ = 3 and H₁: µ 3. Hypotheses are tested using a two-sided t-test and significance level 0.05. (a) Calculate the usual point estimater for the parameters μ and σ² by using the data sets of both group A and group B. (First determine nA+B, A+B and s² A+B using the given information¹ on the data sets.) (b) Test the hypotheses using the data of the group A (α = 0.05). State the p-value of the test and the decision of rejecting or accepting the null hypothesis. (c) Test the hypothesis using the meta data of groups A and B (α = 0.05).

MATLAB: An Introduction with Applications
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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2. Research groups A and B have studied independently a phenomenon that can be described by random sampling from a normal distribution N(μ, σ²), where both parameters are unknown. The interesting parameter is is the population average μ. Results of research groups (sample size, sample mean and sample variance) are respectively nA = 10, NB = 15, A = 3.967, s B = 3.522, s = 1.995, = 1.310. We would like to do meta analysis, i.e. combine the research results of these two groups. We set the hypotheses H₁: µ = 3 and H₁: µ 3. Hypotheses are tested using a two-sided t-test and significance level 0.05. (a) Calculate the usual point estimater for the parameters μ and σ² by using the data sets of both group A and group B. (First determine nA+B, A+B and s² A+B using the given information¹ on the data sets.) (b) Test the hypotheses using the data of the group A (α = 0.05). State the p-value of the test and the decision of rejecting or accepting the null hypothesis. (c) Test the hypothesis using the meta data of groups A and B (α = 0.05).
Transcribed Image Text:2. Research groups A and B have studied independently a phenomenon that can be described by random sampling from a normal distribution N(μ, σ²), where both parameters are unknown. The interesting parameter is is the population average μ. Results of research groups (sample size, sample mean and sample variance) are respectively nA = 10, NB = 15, A = 3.967, s B = 3.522, s = 1.995, = 1.310. We would like to do meta analysis, i.e. combine the research results of these two groups. We set the hypotheses H₁: µ = 3 and H₁: µ 3. Hypotheses are tested using a two-sided t-test and significance level 0.05. (a) Calculate the usual point estimater for the parameters μ and σ² by using the data sets of both group A and group B. (First determine nA+B, A+B and s² A+B using the given information¹ on the data sets.) (b) Test the hypotheses using the data of the group A (α = 0.05). State the p-value of the test and the decision of rejecting or accepting the null hypothesis. (c) Test the hypothesis using the meta data of groups A and B (α = 0.05).
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