A company manufactures steel shafts for use in engines. Assume that the length of the steel shaft is normally distributed. A random sample of 10 shafts produced in the following measurements of their lengths (in centimetres): 20.5 19.8 21.2 20.2 18.9 19.6 20.7 20.1 19.8 19.0 (a) Suppose first that the population standard deviation of the length of the shaft is known. In addition, based on this population standard deviation, the margin of error at a confidence level of 95% for the mean length of the shaft for the sample of size 25 is 0.50. Find and interpret an estimate for the mean length of the shaft based on the above sample of size 10 with 99% confidence. 3 (b) Assume now that the population standard deviation of the length of the shaft is unknown. Based on the above sample of size 10, the margin of error for the mean length of the shaft is 0.51564. Find the critical value and significance level associated with this margin of error. In addition, find and interpret the corresponding confidence interval estimate for the mean length of the shaft. State clearly the level of confidence. (c) One method for judging inconsistencies in the production process is to determine the variance of the length of the shaft. Find and interpret an estimate for the variance of the lengths of the shaft with 90% confidence based on the above sample of size 10.
A company manufactures steel shafts for use in engines. Assume that the length of the steel
shaft is normally distributed. A random sample of 10 shafts produced in the following
measurements of their lengths (in centimetres):
20.5 19.8 21.2 20.2 18.9 19.6 20.7 20.1 19.8
19.0
(a) Suppose first that the population standard deviation of the length of the shaft is known. In
addition, based on this population standard deviation, the margin of error at a confidence
level of 95% for the
interpret an estimate for the mean length of the shaft based on the above sample of size 10
with 99% confidence.
3
(b) Assume now that the population standard deviation of the length of the shaft is unknown.
Based on the above sample of size 10, the margin of error for the mean length of the shaft
is 0.51564. Find the critical value and significance level associated with this margin of
error. In addition, find and interpret the corresponding confidence
mean length of the shaft. State clearly the level of confidence.
(c) One method for judging inconsistencies in the production process is to determine the
variance of the length of the shaft. Find and interpret an estimate for the variance of the
lengths of the shaft with 90% confidence based on the above sample of size 10.
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