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Unformatted text preview: EXERCISES IN STATISTICS
Series A, No. 9 1. The average length of a ﬁnger bone of 10 fossil skeletons of the proconsul
hominid is 3.73cm, and the standard deviation is 0.34cm. Find 80% and 90%
conﬁdence intervals for the mean length of the bone in the species.
2. Mr. Smith has been threatened with the loss of his job if he persists in arriving
late at the oﬃce. Prior to this threat, his average arrival time over 10 days
was 10–46am. with a standard deviation of 16 minutes. For ﬁve working days
since the threat, his arrival time has been 10–01am. with a standard deviation
of 12 mins. Construct a 90% conﬁdence interval for the extent to which Mr.
Smith has improved his arrival time.
3. A factory that manufactures shafts of 5cm diameter has installed new lathes.
Hitherto, the variance of the diameter of the shafts has been 0.49mm2 . A
sample of 20 shafts, produced by the new machines, has a variance of 0.25mm2
measured about the theoretical mean of 5cm. Find a 95% conﬁdence interval
for the new variance, and a 95% conﬁdence interval for the ratio of the old and
the new variances.
4. Two independent random samples of sizes n = 16 and m = 10, taken from
independent normal distributions N (µx , σx ) and N (µy , σy ) yield, respectively,
x = 3.6, sx = 4.14 and y = 13.6, sy = 7.6. Find the 90% conﬁdence interval
for σx /σy when µx and µy are unknown.
P the 90% conﬁdence interval for σx /σy on the assumption that µx = 4
and (xi − µx )2 /n = 5.3 and that µy = 12 and (yi − µy )2 /m = 7.5. 1 ...
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This note was uploaded on 03/02/2012 for the course EC 2019 taught by Professor D.s.g.pollock during the Spring '12 term at Queen Mary, University of London.
- Spring '12