Question

1. Noise pollution is measured in decibels. In California any motorcycle made after 1980 may not be any louder than 80 decibels. Harley Davidson claims their mean decibel rating on bikes is 70 with a variance of 10. The variance of the noise is questioned. Just because Harley has a mean that is less than 80, they could still be producing louder than acceptable bikes. The federal EPA conducts a sample of 30 bikes and determines the variance to be 20 decibels. Is there enough evidence to question Harley’s claim of 10 decibels?

(15pts)

1. Use the Hypothesis Test Method

Answer 1

Result:

Noise pollution is measured in decibels. In California any motorcycle made after 1980 may not be any louder than 80 decibels. Harley Davidson claims their mean decibel rating on bikes is 70 with a variance of 10. The variance of the noise is questioned. Just because Harley has a mean that is less than 80, they could still be producing louder than acceptable bikes. The federal EPA conducts a sample of 30 bikes and determines the variance to be 20 decibels. Is there enough evidence to question Harley’s claim of 10 decibels?

One sample variance test used

Ho: σ2 = 10    Ha: σ2 ≠ 10

= (29*20) / 10 =58.0

DF=30-1=29

Chi square value at 0.05 level,

Lower Critical Value 16.047

Upper Critical Value 45.722

Calculated chi square 58.0 is above Upper Critical Value of 45.722.

The null hypothesis is rejected.

At the 5% level of significance, there is enough evidence to reject the Harley’s claim of 10 decibels.