Question 2: Materials science engineers are developing a carbon fiber composite

Question

Question 2: Materials science engineers are developing a carbon fiber composite material as an alternative to aluminum based subframes for a passenger vehicle. They would like to know the strength of the carbon fiber composite; they strongly believe that the specific strength of the material is normally distributed. Due to limited resources, they conduct 10 tensile tests on 10 samples, and found that the average specific strength is 7.67 MPa/(kg/m3) with a standard deviation of 0.06 MPa/(kg/m). Use this information and answer Question 2a to 2c. Question 2a what is the lower bound of a 98% confidence interval for the true mean of the specific strength of this carbon fiber composite? (Use four decimal places) Question 2b: Later the engineers realized that there was a mistake while calculating the standard deviation. They used population standard deviation equation instead of sample standard deviation equation. How would this affect the half-width of the 96% confidence interval if you use the correct equation? O The halfwidth would not change O The halfwidth would decrease O The halfwidth would increase O There is not enough information to tell Question 2c The engineers were reviewing other researchers' work, and found that one research lab conducted a similar experiment with 8 samples. The average specific strength obtained by these researchers is 7.54 MPa/(kg/m3) with a standard deviation of 0.03. The reported confidence interval is [7.5199, 7.5601, what confidence level was used? Please report your answer as a decimal. (eg, 95% confidence interval 0.95. Use 2 decimal places)

Explanation / Answer

2a) From statistical software output, 98% confidence interval will be:

One sample T summary confidence interval:
: Mean of population

98% confidence interval results:

Therefore,

Lower bound = 7.6165

2 b) The standard deviation will increase and hence, the half width would increase.

Option C is correct.

2 c) Confidence interval used = 90%

So,

The answer is 0.90

Mean Sample Mean Std. Err. DF L. Limit U. Limit 7.67 0.018973666 9 7.616467 7.723533

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