Question

1. A very large population of bipolar transistors has a current gain with a mean value of 120 and a standard deviation of 10. The values of current gain may be assumed to be independent Gaussian random variables. (a) Find the confidence interval for a confidence level of 90% on the sample mean if it is computed from a sample size of 150. (b) Find the confidence interval for a confidence level of 90% on the sample mean if it is computed from a sample size of 21

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Answer 1

1)

a)

mean xbar = 120.000 sample siz n = 150 population std deviation sigma = 10.000 standard error of mean = sigma_x bar = sigma/squareroot n = 0.816 for 90% CI value of Z = 1.645 margin of error E = Z* std error = 1.343 lower confidence bound = sample mean - margin of error = 118.66 upper confidence bound = sample mean + margin of error = 121.34 mean xbar = 120.000 sample size n = 21 population std deviation sigma = 10.000 standard error of mean = sigma_x bar = sigma/ squareroot n = 2.182 for 90% CI value of Z = 1.645 margin of error E = Z* std error = 3.590 lower confidence bound = sample mean - margin of error = 116.41 upper confidence bound = sample mean + margin of error = 123.59

b)