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# Hypothesis testing on low-frequency data

Indoor natatoriums or swimming pools are noted for their pool acoustical properties. The goal is to design a pool in such a way that the average time that it takes a low-frequency sound to die is at most 1.3 seconds with a standard deviation of at most .6 seconds. Computer simulations of a preliminary design are conducted to see whether these standards are exceeded.
These data are obtained on the time required for a low-frequency sound to die:

1.8 2.8 4.6 5.3 6.6 3.7 5.6 0.3 4.3 7.9
5.0 5.9 2.5 3.9 3.6 5.3 2.7 1.3 2.1 2.7
6.1 3.8 4.4 2.3 3.3 0.5 5.9 4.6 7.1 3.3

For these data x bar = 3.97 and s = 1.89.
(a) Test H0 : µ = 1.3 vs H1 : µ > 1.3 at the α = .01 level.
(b) Test H0 : σ = .6 vs H1 : σ > .6 at the α = .01 level. Does it appear that the design speciﬁcations are being met?

#### Solution Preview

Hello student,
hypothesis testing
Indoor natatoriums or swimming pools are noted for their pool acoustical properties. The goal is to design a pool in such a way that the average time that it takes a low-frequency sound to die is at most 1.3 seconds with a standard deviation of at most .6 seconds. Computer simulations of a preliminary design are conducted to see whether these standards are exceeded.
These data are obtained on the time required for a low-frequency sound to die:

1.8 2.8 4.6 5.3 6.6 3.7 5.6 0.3 4.3 7.9 ...

#### Solution Summary

The solution examines hypothesis testing on low-frequency data. The solution determines the design specification being met.

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