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?

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= ?

a)  

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

Step-by-step explanation:

From the question we are told that:

Sample size

Mean

Standard deviation

Significance level is taken as

t test statistics

Therefore

Critical point

Therefore

P-value from T distribution table

Conclusion

We Reject the Null Hypothesis

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

answer: 20

step-by-step explanation:

answer:   expression= p+p*d%

price reduction + sale price = $625

sale price: $p+$p*d%

where d% is the percentage of discount

step-by-step explanation:

original price = p

price went down by $150 price reduction $p*d%

sale price= $ 475

therefore the price before sale is: $625

and the expression that shows the price before sale is: p+p*d%