DEPARTMENT OF MATHEMATICS & STATISTICS
STAT 2593
FINAL EXAMINATION
DECEMBER 1991 TIME: 21
2Hours
THERE ARE SEVEN PROBLEMS, WITH TOTAL VALUE 100 MARKS. PROBLEM 7 IS TO
BE ANSWERED ON A SEPARATE SHEET OF PAPER. MAKE SURE THAT YOU PUT YOUR
NAME ON THIS SHEET AND HAND IT IN.
1. The data in column C1 are measurements on lifetime, in years of normal operation, of a
certain brand of light bulbs.
MTB> print c1
C1
2.75 3.75 3.00 3.25 3.25 3.25 3.25 3.50 3.50 3.75
3.75 3.75 3.75 3.75 4.00 4.00 4.25 4.50 4.75 5.50
MTB > describe c1
N MEAN MEDIAN TRMEAN STDEV SEMEAN
C1 20 3.713 3.750 3.667 0.675 0.151
MIN MAX Q1 Q3
C1 2.750 5.500 3.250 4.000
(a) Give a 90% confidence interval for the mean lifetime for these light bulbs.
(b) Can a consumer group claim that the bulbs last, on average, less than 3.8 years? (Use
your answer to (a) and give a one sentence explanation.)
(c) Give a 90% confidence interval for the standard deviation of lifetime for these bulbs.
(d) Is the median lifetime less than 3.8 years? (Use the sign test.)
2. The data in column C2 are measurements on lifetime of a different brand of light bulb. Is
lifetime of this second brand less variable than lifetime of the brand considered in problem 1?
(Test.)
MTB > describe c2
N MEAN MEDIAN TRMEAN STDEV SEMEAN
C1 15 2.700 2.500 2.692 0.474 0.122
MIN MAX Q1 Q3
C1 2.000 3.500 2.500 3.000
