Polymer composite materials have gained popularity because they have high streng

Question

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.1 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use = 0.05.)

t=8.169

P-value= ?

Explanation / Answer

Here, p-value = P(T > 8.169), where, T follows t-distribution

with (10 - 1) d.f. = 9 d.f.

Thus, p-value = 0.

Since, p-value < level of significance = 0.05, we reject H0.

We conclude that the data provides compelling evidence for

concluding that the true average strength for the WSF/

cellulose composide exceeds 48 MPa.

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