A computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting 12 workers at random and timing each worker on each assembly process. Half of the workers are chosen at random to use Process 1 first, and the rest use Process 2 first. For each worker and each process, the assembly time (in minutes) is recorded, as shown in the table below.Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly times for the two processes differ? Answer this question by performing a hypothesis test regarding μd (which is μ with a letter "d" subscript), the population mean difference in assembly times for the two processes. Assume that this population of differences (Process 1 minus Process 2) is normally distributed.Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If necessary, consult a list of formulas.) A computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Assembly times can vary considerably from workerto worker, and the company decides to eliminate this effect by selecting 12 workers at random and timing each worker on each assembly process. Half of theworkers are chosen at random to use Process 1 first, and the rest use Process 2 first. For each worker and each process, the assembly time (in minutes) isrecorded, as shown in the table below.WorkerProcess 1Process 2Difference(Process 1 - Process 2)Send data to calculator50331727959203534494716475484964934-1 153534848 566191 -13533106271-9114746112775819Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly times for the two processes differ? Answer thisquestion by performing a hypothesis test regarding μd (which is u with a letter "d" subscript), the population mean difference in assembly times for the twoprocesses. Assume that this population of differences (Process 1 minus Process 2) is normally distributed.Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers asspecified. (If necessary, consult a list of formulas.) Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly times for the two processes differ? Answer thisquestion by performing a hypothesis test regarding μ (which is u with a letter "d" subscript), the population mean difference in assembly times for the twoprocesses. Assume that this population of differences (Process 1 minus Process 2) is normally distributed.Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers asspecified. (If necessary, consult a list of formulas.)(a) State the null hypothesis Ho and the alternative hypothesis H₁.Ho :OH₁ U(b) Determine the type of test statistic to use.Type of test statistic: (Choose one)(c) Find the value of the test statistic. (Round to three or more decimal places.)U(d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.)and(e) At the 0.05 level, can the company conclude that the mean assembly times for the two processesdiffer?O Yes O NoμIxX00#0aXS Â0=0 OSO 020рO

For the given data Perform paired t test

A computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting 12 workers at random and timing each worker on each assembly process. Half of the workers are chosen at random to use Process 1 first, and the rest use Process 2 first. For each worker and each process, the assembly time (in minutes) is recorded, as shown in the table below. Worker Process 1 Process 2 Difference (Process 1 Process 2) Send data to calculator 1 50 33 17 2 79 59 20 3 53 44 9 4 71 64 7 5 6 7 8 9 9 48 49 -1 49 34 35 48 34 61 15 1 -13 56 53 3 10 62 71 11 47 12 77 46 58 -9 1 19 Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly times for the two processes differ? Answer this question by performing a hypothesis test regarding μ (which is u with a letter "d" subscript), the population mean difference in assembly times for the two processes. Assume that this population of differences (Process 1 minus Process 2) is normally distributed. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If necessary, consult a list of formulas.)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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A computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Assembly times can vary considerably from worker to worker, and the company decides to eliminate this effect by selecting 12 workers at random and timing each worker on each assembly process. Half of the workers are chosen at random to use Process 1 first, and the rest use Process 2 first. For each worker and each process, the assembly time (in minutes) is recorded, as shown in the table below.

Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly times for the two processes differ? Answer this question by performing a hypothesis test regarding μd (which is μ with a letter "d" subscript), the population mean difference in assembly times for the two processes. Assume that this population of differences (Process 1 minus Process 2) is normally distributed.

Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified. (If necessary, consult a list of formulas.)

A computer manufacturer is interested in comparing assembly times for two keyboard assembly processes. Assembly times can vary considerably from worker
to worker, and the company decides to eliminate this effect by selecting 12 workers at random and timing each worker on each assembly process. Half of the
workers are chosen at random to use Process 1 first, and the rest use Process 2 first. For each worker and each process, the assembly time (in minutes) is
recorded, as shown in the table below.
Worker
Process 1
Process 2
Difference
(Process 1 - Process 2)
Send data to calculator
50
33
17
2
79
59
20
3
53
44
9
4
71
64
7
5
48
49
6
49
34
-1 15
35
34
8
48 56
61
9
1 -13
53
3
10
62
71
-9
11
47
46
1
12
77
58
19
Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly times for the two processes differ? Answer this
question by performing a hypothesis test regarding μd (which is u with a letter "d" subscript), the population mean difference in assembly times for the two
processes. Assume that this population of differences (Process 1 minus Process 2) is normally distributed.
Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as
specified. (If necessary, consult a list of formulas.)

Based on these data, can the company conclude, at the 0.05 level of significance, that the mean assembly times for the two processes differ? Answer this
question by performing a hypothesis test regarding μ (which is u with a letter "d" subscript), the population mean difference in assembly times for the two
processes. Assume that this population of differences (Process 1 minus Process 2) is normally distributed.
Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as
specified. (If necessary, consult a list of formulas.)
(a) State the null hypothesis Ho and the alternative hypothesis H₁.
Ho :O
H₁ U
(b) Determine the type of test statistic to use.
Type of test statistic: (Choose one)
(c) Find the value of the test statistic. (Round to three or more decimal places.)
U
(d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.)
and
(e) At the 0.05 level, can the company conclude that the mean assembly times for the two processes
differ?
O Yes O No
μ
Ix
X
0
0#0
a
X
S Â
0=0 OSO 020
р
O<O
00
S
O<O

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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