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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?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 28E
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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?
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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