3. An accelerated life test is used to estim ate , the mean number of cycles unt

Question

3. An accelerated life test is used to estim ate , the mean number of cycles until failure for an automotive door latch mechanism (a) A confidence interval for this mean was calculated to be (3124.9,3215.7). What was the 2 observed sample mean ()? (b) Someone else used the same sample to attain a confidence interval of (3110.5, 3230.1) One of these confidence intervals has a 95% confidence level and the other has a 99% confidence level. Which interval is the 95% confidence interval? Explain your reasoning. 2 4. The breaking strength of yarn used in manufacturing drapery material has historically had a standard deviation of 2 psi (a) A random sample of n = 30 specimens is selected, with an observed average breaking strength of r = 99.05 psi. Construct a 95% confidence interval for the mean breaking strength. 2 b) This yarn is targeted to have a mean breaking strength of 100psi. What does your 2 confidence interval say about the mean being on-target? (c) The sample standard deviation from the sample was observed to be s2.281. Calcu- late a 95% confidence interval for the population standard deviation , and use this to (4 com ment on the historical assumption that 2 5. The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 circuits is tested, with 13 being found defective. Calculate a 90% upper confidence bound on the population proportion of defective circuits. 3

Explanation / Answer

Observed sample mean is symetrically around the mean

Hence , mean = (3124.9+3215.7)/2 = 3170.3

b.

The 95% confidence interval is (3124.9,3215.7) as the width of this is less than the other one and hemce the person is less confident that the observation would lie within the given width.

PS: We are directed to solve only 1st question if multiple questions are posted

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