Question

In the article “Viscosity Characteristics of Rubber-Modified Asphalts” (J. of Materials in Civil Engr., 1996: 153–156.), a random sample of 5 asphalt specimens of a certain grade of asphalt with 18% rubber added gave the following observations on stabilized viscosity (cP):

2781 2900 3013 2856 2888

Assume that the stabilized viscosity follows a normal distribution. Suppose that for a particular application, it is required that the true mean viscosity be 3000 cP. Use the five-step format to test whether this requirement has been satisfied at the α = 0.05 significance level AND make a conclusion within the context of the problem.

"5 Step Format"

1. State H0 and Ha.

2. State α.

3. State the form of the 1 − α confidence interval you will use, along with all the assumptions necessary.

4. Calculate the 1 − α confidence interval.

5. Based on the 1 − α confidence interval, either: ❑ Reject H0 and conclude Ha, or ❑ Fail to reject H0.

Answer 1

Population viscosity mean is 3000

1.

H0: =3000

H0: 3000

2.

= 0.05

3.

(1-0.05) * 100% or 95 % confidence interval for is [ - t/2 =0.025,4 *S , + t/2 =0.025,4 *S ]

4.

=(2781+ 2900+ 3013 +2856 + 2888) /5 = 2887.6

Sample standard deviation = S= 84.0256

95 % confidence interval for is [2887.6 - 2.776 * 84.0256 , 2887.6 + 2.776 * 84.0256 ] =[2654.345, 3120.855]

5.

Since this interval includes 3000, we fail to reject null hypothesis.

So true viscosity mean is 3000.

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