A personal 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 a random sample of 8 workers 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 Table 1. Worker Process 1 Process 2 Difference(Process 1 - Process 2) 1 46 20 26 2 36 10 26 3 43 43 0 4 61 52 9 5 66 58 8 6 61 62 -1 7 65 49 16 8 72 53 19 Table 1 Based on these data, can the company conclude, at the 0.10 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 fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic:(Round to at least three decimal places.) The two critical values at the 0.10 level of significance:(Round to at least three decimal places.) and At the 0.10 level, can the company conclude that the mean assembly times for the two processes differ?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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A personal 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 a random sample of

workers 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 Table 1.

Worker	Process 1	Process 2	Difference (Process 1 - Process 2)
1	46	20	26
2	36	10	26
3	43	43	0
4	61	52	9
5	66	58	8
6	61	62	-1
7	65	49	16
8	72	53	19

Table 1

Based on these data, can the company conclude, at the

0.10

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

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 fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one)ZtChi squareF

The value of the test statistic: (Round to at least three decimal places.)
The two critical values at the 0.10 level of significance: (Round to at least three decimal places.)	and
At the 0.10 level, can the company conclude that the mean assembly times for the two processes differ?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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