Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 5.4, Problem 11E
In a study of the effect of cooling rate on the hardness of welded joints, 50 welds cooled at a rate of 10°C/s had an average Rockwell (B) hardness of 91.1 and a standard deviation of 6.23, and 40 welds cooled at a rate of 30°C/s had an average hardness of 90.7 and a standard deviation of 4.34.
- a. Find a 95% confidence interval for the difference in hardness between welds cooled at the different rates.
- b. Someone says that the cooling rate has no effect on the hardness. Do these data contradict this claim? Explain.
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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 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 51.4 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 a = 0.05.)
State the appropriate hypotheses.
O H,: H 48
H:u = 48
O H,: = 48
Hi u 48
OH:= 48
H: u + 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.)
P-value =
What can you conclude?
O The data provides compelling…
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 1.3. 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.)
USE SALT
State the appropriate hypotheses.
ⒸHO: μ> 48
H₂: μ = 48
Ho: μ 48
Ho: μ = 48
H₂: 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?
O The data provides compelling…
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 51.3 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.
ⒸH₂: μ = 48
Ha: > 48
Ho:μ = 48
H₂H 48
H₂: μ = 48
Ho: μ< 48
H₂₁:μ = 48
USE SALT
Ho: M = 48
H₂:48
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= 7.68
X
P-value =
Chapter 5 Solutions
Statistics for Engineers and Scientists
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