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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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	85	68	17
2	64	61	3
3	60	30	30
4	64	40	24
5	60	48	12
6	52	26	26
7	43	51	-8
8	76	56	20

Table 1

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

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.

The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one) Z t Chi square F

The value of the test statistic: (Round to at least three decimal places.)
The two critical values at the 0.05 level of significance: (Round to at least three decimal places.)	and
At the 0.05 level, can the company conclude that the mean assembly times for the two processes differ?	Yes	No

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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