Consider the following sample observations on stabilized vis

Consider the following sample observations on stabilized viscosity of asphalt specimens.

Suppose that for a particular application, it is required that true average viscosity be 3000. Does this requirement appear to have been satisfied? State the appropriate hypotheses. (Use ? = 0.05.)

H₀: ? < 3000

H_a: ? = 3000

H₀: ? = 3000

H_a: ? ? 3000

H₀: ? ? 3000

H_a: ? = 3000

H₀: ? > 3000

H_a: ? < 3000

Test the appropriate hypotheses. (Round your answers to three decimal places.)

Solution

H₀: mu = 3000

H_a: mu not equal to 3000

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sample size n=5

sample mean=2884.4

sample standard deviation =82.84805

The test statistic is

t=(2884.4-3000)/(82.84805/sqrt(5))

=-3.120

The degree of freedom =n-1=5-1=4

It is a two-tailed test.

Given a=0.05, the critical values are t(0.025, df=4) =-2.776 or 2.776 (from student t table)

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Reject the null hypothesis. There is sufficient evidence to conclude that the true average is viscosity differs from 3000.