Polymer composite materials have gained popularitybecause they have high strength to weight ratios and arerelatively easy and inexpensive to manufacture. However,their nondegradable nature has prompted development ofenvironmentally friendly composites using natural mate-rials. The article “Properties of Waste Silk ShortFiber/Cellulose Green Composite Films” (J. ofComposite Materials, 2012: 123–127) reported that fora sample of 10 specimens with 2% fiber content, thesample mean tensile strength (MPa) was 51.3 and thesample standard deviation was 1.2. Suppose the trueaverage strength for 0% fibers (pure cellulose) is knownto be 48 MPa. Does the data provide compelling evi-dence for concluding that true average strength for theWSF/cellulose composite exceeds this value?

To determine if there is compelling evidence to conclude that the true average strength for the WSF/cellulose composite exceeds the known value of 48 MPa for pure cellulose, we can perform a hypothesis test.

Step 1: State the null and alternative hypotheses:

• Null hypothesis (H0): The true average strength for the WSF/cellulose composite is equal to or less than 48 MPa.
• Alternative hypothesis (Ha): The true average strength for the WSF/cellulose composite exceeds 48 MPa.

Step 2: Choose a significance level: We need to choose a significance level (alpha) to determine the threshold for rejecting the null hypothesis. Let's assume a significance level of 0.05.

Step 3: Calculate the test statistic: We can calculate the test statistic using the sample mean, sample standard deviation, sample size, and the known value for pure cellulose. The test statistic formula for a one-sample t-test is: t = (sample mean - known value) / (sample standard deviation / sqrt(sample size))

In this case, the sample mean is 51.3, the known value is 48, the sample standard deviation is 1.2, and the sample size is 10. Plugging these values into the formula, we can calculate the test statistic.

Step 4: Determine the critical value: We need to determine the critical value for the t-distribution with (sample size - 1) degrees of freedom at the chosen significance level. Using a t-table or a statistical software, we can find the critical value.

Step 5: Compare the test statistic with the critical value: If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Step 6: Draw a conclusion: Based on the comparison of the test statistic and the critical value, we can draw a conclusion. If we reject the null hypothesis, it provides compelling evidence to conclude that the true average strength for the WSF/cellulose composite exceeds the known value of 48 MPa. If we fail to reject the null hypothesis, there is not enough evidence to support the claim that the true average strength exceeds 48 MPa.

Please note that the actual calculations for the test statistic and critical value are not provided in the given question, so you would need to perform those calculations to reach a conclusion.