A machine is designed to fill each container with 300 ml of fruit juice. It may be assumed that the volume of fruit juices in a container follows a normal distribution. A random sample of 12 containers has a sample mean of 291 ml and a sample standard deviation of 8 ml. Let denote the mean volume of fruit juice in a container that is filled by the machine. (a) Carry out a two-tailed test of the null hypothesis Ho : μ = 300 versus the alternative H₁:300 with the level of significance a = 5%. Consider the following Confidence Intervals: Confidence Interval A: (294.9, 305.1) Confidence Interval B: (285.9, 296.1) Confidence Interval C: (295.5, 304.5) Which of the above Confidence Intervals, if any, is the 95% confidence interval that can be used for the test? Enter A, B or C in the answer box for Confidence Intervals A, B or C respectively. If none of them is the correct Confidence Interval, enter N in the answer box. Answer: N (b) What is the conclusion of the test? In the answer box, enter R for 'reject Ho' and DNR for 'do not reject Ho'. If the test is inconclusive, enter N. Answer: R (c) What is the p-value of the test? Give your answer to 3 decimal places in the answer box. Answer: 0.002
A machine is designed to fill each container with 300 ml of fruit juice. It may be assumed that the volume of fruit juices in a container follows a normal distribution. A random sample of 12 containers has a sample mean of 291 ml and a sample standard deviation of 8 ml. Let denote the mean volume of fruit juice in a container that is filled by the machine. (a) Carry out a two-tailed test of the null hypothesis Ho : μ = 300 versus the alternative H₁:300 with the level of significance a = 5%. Consider the following Confidence Intervals: Confidence Interval A: (294.9, 305.1) Confidence Interval B: (285.9, 296.1) Confidence Interval C: (295.5, 304.5) Which of the above Confidence Intervals, if any, is the 95% confidence interval that can be used for the test? Enter A, B or C in the answer box for Confidence Intervals A, B or C respectively. If none of them is the correct Confidence Interval, enter N in the answer box. Answer: N (b) What is the conclusion of the test? In the answer box, enter R for 'reject Ho' and DNR for 'do not reject Ho'. If the test is inconclusive, enter N. Answer: R (c) What is the p-value of the test? Give your answer to 3 decimal places in the answer box. Answer: 0.002
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
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Transcribed Image Text:A machine is designed to fill each container with 300 ml of fruit
juice. It may be assumed that the volume of fruit juices in a
container follows a normal distribution. A random sample of 12
containers has a sample mean of 291 ml and a sample standard
deviation of 8 ml. Let u denote the mean volume of fruit juice in a
container that is filled by the machine.
(a) Carry out a two-tailed test of the null hypothesis
Ho : μ = 300 versus the alternative H₁ : μ 300 with the
level of significance a = 5%. Consider the following Confidence
Intervals:
Confidence Interval A: (294.9, 305.1)
Confidence Interval B: (285.9, 296.1)
Confidence Interval C: (295.5, 304.5)
Which of the above Confidence Intervals, if any, is the 95%
confidence interval that can be used for the test? Enter A, B or C
in the answer box for Confidence Intervals A, B or C respectively.
If none of them is the correct Confidence Interval, enter N in the
answer box.
Answer:
N
(b) What is the conclusion of the test? In the answer box, enter R
for 'reject Ho' and DNR for 'do not reject Ho'. If the test is
inconclusive, enter N.
Answer: R
(c) What is the p-value of the test? Give your answer to 3
decimal places in the answer box.
Answer:
0.002
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