Suppose that the results of carrying out the hypothesis test lead to non-rejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean age at diagnosis of all people with early-onset dementia is less than 55 years old. Suppose that the manufacturer of a new COVID-19 vaccine in South Africa wants to test the null hypothesis Ho: 0= 0.90 against the alternative hypothesis H₁:0 = 0.60. She defined her test statistic Y as a number of patients recovered from COVID-19 after an observed twenty trials. If she decided to accept H, and assume y > 14, i) What will be her Type I error and the power of the test. ii) Explain how the probability of Type II error can be reduced in this case and how it will affect Type I error. Give a practical example.
Suppose that the results of carrying out the hypothesis test lead to non-rejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean age at diagnosis of all people with early-onset dementia is less than 55 years old. Suppose that the manufacturer of a new COVID-19 vaccine in South Africa wants to test the null hypothesis Ho: 0= 0.90 against the alternative hypothesis H₁:0 = 0.60. She defined her test statistic Y as a number of patients recovered from COVID-19 after an observed twenty trials. If she decided to accept H, and assume y > 14, i) What will be her Type I error and the power of the test. ii) Explain how the probability of Type II error can be reduced in this case and how it will affect Type I error. Give a practical example.
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
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
Related questions
Question
![c)
Suppose that the results of carrying out the hypothesis test lead to non-rejection of the null
hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean
age at diagnosis of all people with early-onset dementia is less than 55 years old. Suppose
that the manufacturer of a new COVID-19 vaccine in South Africa wants to test the null
hypothesis Ho: 0= 0.90 against the alternative hypothesis H₁:0 = 0.60. She defined her test
statistic Y as a number of patients recovered from COVID-19 after an observed twenty trials.
If she decided to accept H, and assume y > 14,
i) What will be her Type I error and the power of the test.
ii) Explain how the probability of Type II error can be reduced in this case and how it will affect
Type I error. Give a practical example.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22a90258-704b-4ee7-9627-b1f4148d4c31%2F1d50855c-20b8-46f3-9e22-11cade63ced9%2Fh3gzrpe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:c)
Suppose that the results of carrying out the hypothesis test lead to non-rejection of the null
hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean
age at diagnosis of all people with early-onset dementia is less than 55 years old. Suppose
that the manufacturer of a new COVID-19 vaccine in South Africa wants to test the null
hypothesis Ho: 0= 0.90 against the alternative hypothesis H₁:0 = 0.60. She defined her test
statistic Y as a number of patients recovered from COVID-19 after an observed twenty trials.
If she decided to accept H, and assume y > 14,
i) What will be her Type I error and the power of the test.
ii) Explain how the probability of Type II error can be reduced in this case and how it will affect
Type I error. Give a practical example.
![c)
Suppose that the results of carrying out the hypothesis test lead to non-rejection of the null
hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean
age at diagnosis of all people with early-onset dementia is less than 55 years old. Suppose
that the manufacturer of a new COVID-19 vaccine in South Africa wants to test the null
hypothesis Ho: 0= 0.90 against the alternative hypothesis H₁:0 = 0.60. She defined her test
statistic Y as a number of patients recovered from COVID-19 after an observed twenty trials.
If she decided to accept H, and assume y > 14,
i) What will be her Type I error and the power of the test.
ii) Explain how the probability of Type II error can be reduced in this case and how it will affect
Type I error. Give a practical example.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22a90258-704b-4ee7-9627-b1f4148d4c31%2F1d50855c-20b8-46f3-9e22-11cade63ced9%2Fsnaprrp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:c)
Suppose that the results of carrying out the hypothesis test lead to non-rejection of the null
hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean
age at diagnosis of all people with early-onset dementia is less than 55 years old. Suppose
that the manufacturer of a new COVID-19 vaccine in South Africa wants to test the null
hypothesis Ho: 0= 0.90 against the alternative hypothesis H₁:0 = 0.60. She defined her test
statistic Y as a number of patients recovered from COVID-19 after an observed twenty trials.
If she decided to accept H, and assume y > 14,
i) What will be her Type I error and the power of the test.
ii) Explain how the probability of Type II error can be reduced in this case and how it will affect
Type I error. Give a practical example.
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