7.15 A soft-drink firm is evaluating an investment in a new type of canning machine. The company has already determined that it will be able to fill more cans per day for the same cost if the new machines are installed. However, it must determine the variability of fills using the new machines and wants the variability from the new machines to be equal to or smaller than that currently obtained using the old machines. A study is designed in which random samples of 40 cans are selected from the output of both types of machines and the amount of fill (in ounces) is determined. The data are given below. Old Machine 16.74 15.75 16.19 16.54 15.92 16.29 16.44 16.29 16.38 16.47 16.56 16.42 16.08 16.47 16.02 16.74 15.97 16.47 16.06 16.64 16.40 16.40 16.28 16.66 16.80 16.36 16.36 16.27 16.43 16.26 16.31 16.59 16.24 16.63 16.15 16.17 16.32 16.81 16.27 17.09 New Machine 15.64 15.81 16.20 16.36 16.36 16.05 16.07 16.04 16.08 16.31 16.50 16.14 16.12 16.30 16.41 16.11 16.20 16.29 15.75 16.22 16.12 16.23 16.19 16.59 16.08 16.07 16.15 16.50 16.25 16.25 16.19 16.13 15.96 16.02 16.29 15.99 15.99 16.42 16.15 16.23 a. Estimate the standard deviations in fill for types of machines using 95% confidence intervals. b. Do these data present sufficient evidence to indicate that the new type of machine has less variability of fills than the old machine?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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7.15

A soft-drink firm is evaluating an investment in a new type of canning machine. The company has already determined that it will be able to fill more cans per day for the same cost if the new machines are installed. However, it must determine the variability of fills using the new machines and wants the variability from the new machines to be equal to or smaller than that currently obtained using the old machines. A study is designed in which random samples of 40 cans are selected from the output of both types of machines and the amount of fill (in ounces) is determined. The data are given below.

Old Machine

16.74	15.75	16.19	16.54	15.92	16.29	16.44	16.29
16.38	16.47	16.56	16.42	16.08	16.47	16.02	16.74
15.97	16.47	16.06	16.64	16.40	16.40	16.28	16.66
16.80	16.36	16.36	16.27	16.43	16.26	16.31	16.59
16.24	16.63	16.15	16.17	16.32	16.81	16.27	17.09

New Machine

15.64	15.81	16.20	16.36	16.36	16.05	16.07	16.04
16.08	16.31	16.50	16.14	16.12	16.30	16.41	16.11
16.20	16.29	15.75	16.22	16.12	16.23	16.19	16.59
16.08	16.07	16.15	16.50	16.25	16.25	16.19	16.13
15.96	16.02	16.29	15.99	15.99	16.42	16.15	16.23

a. Estimate the standard deviations in fill for types of machines using 95% confidence intervals.

b. Do these data present sufficient evidence to indicate that the new type of machine has less variability of fills than the old machine?

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