Question #4 An article in Food Testing and Analysis measured the sugar concentration (Brix) in clear apple juice. All readings were taken at 20°C: 11.48 11.45 11.48 11.47 11.48 11.50 11.42 11.49 11.45 11.44 11.45 11.47 11.46 11.47 11.43 11.50 11.49 11.45 11.46 11.47 (a) Test the hypothesis Ho:u=11.5 versus H1:µ#11.5 using a=0.05. Find the P-value. (b) Compute the power of the test if the true mean is 11.4. (c) What sample size would be required to detect a true mean sugar concentration of 11.45 if we wanted the power of the test to be at least 0.9?

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Question #4
An article in Food Testing and Analysis measured the sugar concentration (Brix) in clear apple
juice. All readings were taken at 20°C:
11.48 11.45 11.48 11.47 11.48
11.50 11.42 11.49 11.45 11.44
11.45 11.47 11.46 11.47 11.43
11.50 11.49 11.45 11.46 11.47
(a) Test the hypothesis Ho:u=11.5 versus H1:µ+11.5 using a=0.05. Find the P-value.
(b) Compute the power of the test if the true mean is 11.4.
(c) What sample size would be required to detect a true mean sugar concentration of 11.45 if we
wanted the power of the test to be at least 0.9?
(d) Explain how the question in part (a) could be answered by constructing a two-sided
confidence interval on the mean sugar concentration.
Transcribed Image Text:Question #4 An article in Food Testing and Analysis measured the sugar concentration (Brix) in clear apple juice. All readings were taken at 20°C: 11.48 11.45 11.48 11.47 11.48 11.50 11.42 11.49 11.45 11.44 11.45 11.47 11.46 11.47 11.43 11.50 11.49 11.45 11.46 11.47 (a) Test the hypothesis Ho:u=11.5 versus H1:µ+11.5 using a=0.05. Find the P-value. (b) Compute the power of the test if the true mean is 11.4. (c) What sample size would be required to detect a true mean sugar concentration of 11.45 if we wanted the power of the test to be at least 0.9? (d) Explain how the question in part (a) could be answered by constructing a two-sided confidence interval on the mean sugar concentration.
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