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 51.7 and the sample standard deviation was 1.4. 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.)

State the appropriate hypotheses.

a)H₀: μ = 48 H_a: μ ≠ 48

b)H₀: μ < 48 H_a: μ = 48   

c)H₀: μ = 48 H_a: μ < 48

d)H₀: μ > 48 H_a: μ = 48

e)H₀: μ = 48 H_a: μ > 48

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
P-value	=

What can you conclude?

a)The data provides compelling evidence that the true average strength for the WSF/cellulose composite exceeds 48.

b)The data does not provide compelling evidence that the true average strength for the WSF/cellulose composite exceeds 48.    

Answer 1

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