Question

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.

a. Does this requirement appear to have been satisfied? State and test the appropriate hypothesis. (α=0.05)

b. Find the P-value.

c. Calculate the CI and use it to test the hypothesis in part a.

Answer 1

$\bar x$ = 2887.6

s = 84.0238

A) H0 : $\mu$ = 3000

Ha : $\mu \neq$ 3000

At alpha = 0.05, the critical values are t^* = +/- 2.777

The test statistic t = ( $\bar x - \mu$ )/(s/ $\sqrt n$ )

= (2887.6 - 3000)/(84.0238/ $\sqrt 5$ )

= -2.99

As the test statistic value is less than the lower critical value (-2.99 < -2.777), we should reject the null hypothesis.

So this requirement doesn't appear to have been satisfied.

B) P-value = 2 * P(T < -2.99)

= 2 * 0.0202

= 0.0404

C) The 95% confidence interval is

$\bar x$ +/- t^* * s/ $\sqrt n$

= 2887.6 +/- 2.777 * 84.0238/ $\sqrt 5$

= 2887.6 +/- 104.35

= 2783.25, 2991.95

As the confidence interval doesn't cointain 0, we should reject the null hypothesis.

So this requirement doesn't appear to have been satisfied.