3. According to a claim made by person A that the lengths of the earth worms liv- ing on their backyard follow normal distribution with expected value exceeding 50 (cm). An independent researcher measures the earth worms living on the backyard (n = 50) and obtains the following results in the length measurement: = 45.5 and s² 389.2. Your task is to act as an expert and help to find out if the claim seems exaggerated. Let us, therefore, assume that the random variables Y₁, ..., Yn corresponding to the observations y₁,..., Yn made by the independent observer are independent and follow the distribution N(μ, σ²), where both parameters are inde- pendent and o² > 0. = (a) Generate an ML estimate and a 95% symmetric confidence interval for the parameter μ. (b) Form a suitable test statistics for which you can test the null hypothesis Ho: μ = 50. What is the alternative hypothesis H₁ in this case? (c) Calculate the p value of the test. Does the test reject the null hypothesis with level of significance a = 0.05? What if we choose a = 0.01? (d) Based on the previous, what do you think about the claim made by A and what are your suggestions what should be done for possible further investigations on the matter?
3. According to a claim made by person A that the lengths of the earth worms liv- ing on their backyard follow normal distribution with expected value exceeding 50 (cm). An independent researcher measures the earth worms living on the backyard (n = 50) and obtains the following results in the length measurement: = 45.5 and s² 389.2. Your task is to act as an expert and help to find out if the claim seems exaggerated. Let us, therefore, assume that the random variables Y₁, ..., Yn corresponding to the observations y₁,..., Yn made by the independent observer are independent and follow the distribution N(μ, σ²), where both parameters are inde- pendent and o² > 0. = (a) Generate an ML estimate and a 95% symmetric confidence interval for the parameter μ. (b) Form a suitable test statistics for which you can test the null hypothesis Ho: μ = 50. What is the alternative hypothesis H₁ in this case? (c) Calculate the p value of the test. Does the test reject the null hypothesis with level of significance a = 0.05? What if we choose a = 0.01? (d) Based on the previous, what do you think about the claim made by A and what are your suggestions what should be done for possible further investigations on the matter?
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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Question
Transcribed Image Text:3. According to a claim made by person A that the lengths of the earth worms liv-
ing on their backyard follow normal distribution with expected value exceeding 50
(cm). An independent researcher measures the earth worms living on the backyard
(n = 50) and obtains the following results in the length measurement: = 45.5
and s²
389.2. Your task is to act as an expert and help to find out if the claim
seems exaggerated. Let us, therefore, assume that the random variables Y₁, ..., Yn
corresponding to the observations y₁,..., Yn made by the independent observer are
independent and follow the distribution N(μ, σ²), where both parameters are inde-
pendent and o² > 0.
=
(a) Generate an ML estimate and a 95% symmetric confidence interval for the
parameter μ.
(b) Form a suitable test statistics for which you can test the null hypothesis Ho:
μ = 50. What is the alternative hypothesis H₁ in this case?
(c) Calculate the p value of the test. Does the test reject the null hypothesis with
level of significance a = 0.05? What if we choose a = 0.01?
(d) Based on the previous, what do you think about the claim made by A and what
are your suggestions what should be done for possible further investigations on
the matter?
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