MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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 the 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 51.8 and the sample standard deviation was 1.5. 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 the true average strength for the WSF/cellulose composite exceeds this value? (Use \(\alpha = 0.05\).)

**Hypotheses:**

1. \(H_0: \mu = 48\)
2. \(H_a: \mu > 48\)

**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.)

- \(t =\) [Input box]
- \(P\)-value = [Input box]

**Conclusion:**

- The data provides compelling evidence that the true average strength for the WSF/cellulose composite exceeds 48.
- The data does not provide compelling evidence that the true average strength for the WSF/cellulose composite exceeds 48.
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Transcribed Image Text: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 the 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 51.8 and the sample standard deviation was 1.5. 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 the true average strength for the WSF/cellulose composite exceeds this value? (Use \(\alpha = 0.05\).) **Hypotheses:** 1. \(H_0: \mu = 48\) 2. \(H_a: \mu > 48\) **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.) - \(t =\) [Input box] - \(P\)-value = [Input box] **Conclusion:** - The data provides compelling evidence that the true average strength for the WSF/cellulose composite exceeds 48. - The data does not provide compelling evidence that the true average strength for the WSF/cellulose composite exceeds 48.
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