Question

Consider the following sample observations on stabilized viscosity of asphalt specimens. 2755 2892 3013 2857 2887 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 a = 0.05.) Ho: > 3000 Hall < 3000 Ho: u < 3000 Hou = 3000 Ho: 4 = 3000 Ha: 4 = 3000 Hou = 3000 Ha: 4 = 3000 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) P-value = What can you conclude? Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average is viscosity differs from 3000. Reject the null hypothesis. There is sufficient evidence to conclude that the true average is viscosity differs from 3000. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average is viscosity differs from 3000. Reject the null hypothesis. There is not sufficient evidence to conclude that the true average is viscosity differs from 3000.

Answer 1

Average of the given sample = 2881, hence the requirement of average viscosity of 3000 does not appear to have been satisfied.

The hypotheses are:

H₀: $\mu$ = 3000

H_a: $\mu$ != 3000

Test statistic, t = [ x̄ - μ ] / [ s / sqrt( n ) ], where x̄ is the sample mean, s is the sample std deviation and $\mu$ is the hypothesized population mean.

=> t = (2881 - 3000) / (92.24 / sqrt(5)) = - 2.885

And, p-value = 0.0224

Since p-value < 0.05, we cannot reject the null hypothesis at the 5% significance level. Hence, there is sufficient evidence to conclude that the true viscosity differs from 3000. (Option b)