Question

The sample observations on stabilized viscosity of asphalt specimens are 2781, 2900, 3013, 2856 and 2888. Suppose that for a particular application, it is required that true average viscosity be 3000. Does this requirement appear to have been satisfied? State and test the appropriate hypothesis at alpha = 0.05.

Answer 1

Answer:

There is no enough evidence that the viscosity is not 3000. The viscosity is not significantly different from 3000.

Step-by-step explanation:

We have to perform an hypothesis test on the mean.

The null and alternative hypothesis are:

$H_0: \mu=3000\\\\H_1:\mu\neq3000$

The significance level is 0.05.

The mean of the sample is:

$M=(1/5)*(2781+2900+3013+2856+2888)=2887.6$

The standard deviation of the sample is:

$s=\sqrt{\frac{1}{5-1}*[(2781-2887.6)^2 +(2900-2887.6)^2 +...]}=84.0$

The statistic t can be calculated as:

$t=\frac{M-\mu}{s} =\frac{2887.6-3000}{84} =-1.338$

The degrees of freedom are $df=N-1=5-1=4$

The P-value for t=-1.338 and df=4 is P=0.2519. The P-value is greater than the significance level, so it failed to reject the null hypothesis.

There is no enough evidence that the viscosity is not 3000.