3. [Management Decision] Management must make a decision concerning the adoption of either plan I or plan II for workers. Under plan I, workers will be given a 15-minute coffee break in the afternoon; whereas, under plan II, workers are dismissed 15 minutes earlier in the day. As input to the decision-making process, a test of hypotheses was set up to compare the average productivity µi of workers under plan I versus the average productivity µ2 under plan II. A random sample of n1 = 10 workers was assigned to plan I, and a random sample of n2 = 12 workers was assigned to plan II. Both groups were assigned to identical tasks on the last stages of an assembly line that produces ball bearings. Productivity is measured in terms of the quantity of ball bearings produced. It was found that the sample mean of productivity for the first group ã1 = 98 units of ball bearings, and the sample standard deviation was s1 = 5. For the second group, the sample mean was 2 = 100 and the sample standard deviation was s2 = 4. It was claimed that plan II has a higher productivity. How do you set up the two competing hypotheses for this test? Assuming that the productivities under the two plans have equal though unknown variances. Calculate the pooled sample standard deviation. Show your work. Please keep the second decimal place in your answer.
3. [Management Decision] Management must make a decision concerning the adoption of either plan I or plan II for workers. Under plan I, workers will be given a 15-minute coffee break in the afternoon; whereas, under plan II, workers are dismissed 15 minutes earlier in the day. As input to the decision-making process, a test of hypotheses was set up to compare the average productivity µi of workers under plan I versus the average productivity µ2 under plan II. A random sample of n1 = 10 workers was assigned to plan I, and a random sample of n2 = 12 workers was assigned to plan II. Both groups were assigned to identical tasks on the last stages of an assembly line that produces ball bearings. Productivity is measured in terms of the quantity of ball bearings produced. It was found that the sample mean of productivity for the first group ã1 = 98 units of ball bearings, and the sample standard deviation was s1 = 5. For the second group, the sample mean was 2 = 100 and the sample standard deviation was s2 = 4. It was claimed that plan II has a higher productivity. How do you set up the two competing hypotheses for this test? Assuming that the productivities under the two plans have equal though unknown variances. Calculate the pooled sample standard deviation. Show your work. Please keep the second decimal place in your answer.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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![3. [Management Decision]
Management must make a decision concerning the adoption of either plan I or plan II for workers. Under plan
I, workers will be given a 15-minute coffee break in the afternoon; whereas, under plan II, workers are dismissed
15 minutes earlier in the day. As input to the decision-making process, a test of hypotheses was set up to
compare the average productivity µi of workers under plan I versus the average productivity H2 under plan II.
A random sample of n1 = 10 workers was assigned to plan I, and a random sample of n2 = 12 workers was
assigned to plan II. Both groups were assigned to identical tasks on the last stages of an assembly line that
produces ball bearings. Productivity is measured in terms of the quantity of ball bearings produced. It was
found that the sample mean of productivity for the first group ã1 = 98 units of ball bearings, and the sample
standard deviation was s1 = 5. For the second group, the sample mean was 2 = 100 and the sample standard
deviation was s2 = 4.
It was claimed that plan II has a higher productivity. How do you set up the two competing
hypotheses for this test?
Assuming that the productivities under the two plans have equal though unknown variances.
Calculate the pooled sample standard deviation. Show your work. Please keep the second decimal place
in your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42f9d7c6-4c7a-44ab-8c36-1d379ff2d1eb%2F7c41e246-a39a-4b00-8668-7d6928a7a7c2%2Favmqvvp_processed.png&w=3840&q=75)
Transcribed Image Text:3. [Management Decision]
Management must make a decision concerning the adoption of either plan I or plan II for workers. Under plan
I, workers will be given a 15-minute coffee break in the afternoon; whereas, under plan II, workers are dismissed
15 minutes earlier in the day. As input to the decision-making process, a test of hypotheses was set up to
compare the average productivity µi of workers under plan I versus the average productivity H2 under plan II.
A random sample of n1 = 10 workers was assigned to plan I, and a random sample of n2 = 12 workers was
assigned to plan II. Both groups were assigned to identical tasks on the last stages of an assembly line that
produces ball bearings. Productivity is measured in terms of the quantity of ball bearings produced. It was
found that the sample mean of productivity for the first group ã1 = 98 units of ball bearings, and the sample
standard deviation was s1 = 5. For the second group, the sample mean was 2 = 100 and the sample standard
deviation was s2 = 4.
It was claimed that plan II has a higher productivity. How do you set up the two competing
hypotheses for this test?
Assuming that the productivities under the two plans have equal though unknown variances.
Calculate the pooled sample standard deviation. Show your work. Please keep the second decimal place
in your answer.
Transcribed Image Text:Write down the formula of the statistic for the test and calculate the value of the test statistic
based on the observed data. Please keep the second decimal place in your answer.
Please use the t-table provided at the end of this exam to find a range of the p-value for your test
statistic.
Do you think the data provide evidence to support the claim that plan II has higher productivity
than plan I, with the significance level a = 0.05? Why or why not?
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