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. The article "Properties of Waste Silk Shod Fiber/Cellulose Green Composite Films" (. of Composite Materials, 2012: 123-127) reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.3 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?

Answer 1

Complete 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 α = 0.05.)

t=8.169

P-value= ?

Answer:

a)
`P-value=0`

b) Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.

Explanation:

From the question we are told that:

Sample size
`n=10`

Mean
`\=x= 51.3`

Standard deviation
`\sigma=1.2`

Significance level is taken as
`\alpha=0.05`

t test statistics

`t=8.169`

Therefore

`P-Value=P(t>8.169)`

Critical point

`t_(\alpha,df)`

`\alpha=0.05`

`df=10-1=>9`

Therefore

P-value from T distribution table

`P-value=0`

Conclusion

`P-value (0)< \alpha(0.05)`

We Reject the Null Hypothesis
`H_0`

Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.