In: Statistics and Probability
Question ( 4 )
The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed. A random sample of 15 devices is selected and found to have an average life of 5625.1 hours and a sample standard deviation of 226.1 hours.
Test the hypothesis that the true mean life of a biomedical device is greater than 5500
Verify your inference using the P-value approach.
Construct a 95% lower confidence bound on the mean and use it to test the hypothesis.
Suppose that if the mean life is as long as 5400 hours, the engineer would like to detect this difference with probability at least 0.90. Was the sample size n = 15 used in part (a) adequate? Use the sample standard deviation s as an estimate of σ in reaching your decision. Estimate what sample size is needed to detect this difference.