Problem No.
1
(a)
A manufacturer of VCR systems would like to estimate the mean failure time of a
VCR brand with 95% confidence.
Six systems are tested to failure, and the
following data (in hours of playing time) are obtained: 1250, 1320, 1542, 1464,
1275, and 1383.
Estimate the population mean and the 95% confidence interval
on the mean.
(This a small number of data points so you will want to use the
Student’s t function for these estimates).
(b)
To reduce the 95% confidence interval to ± 50 hours, the VCR manufacturer
decides to test more systems to failure.
Determine how many more systems
should be tested.
(If this is a small number you may need to iterate with the
Student’s t function to arrive at you answer).
Solution (a):
Because the sample size is small (n < 30), we should use the tdistribution to estimate the
confidence interval.
But first we have to calculate the mean and (sample) standard deviation
of the data.
x
mean
1250
1320
+
1542
+
1464
+
1275
+
1383
+
6
:=
x
mean
1.372
10
3
×
=
hours
x
x
mean
:=
S
1250
x
−
(
)
2
1320
x
−
(
)
2
+
1542
x
−
(
)
2
+
1464
x
−
(
)
2
+
1275
x
−
(
)
2
+
1383
x
−
(
)
2
+
6
1
−
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 Spring '07
 MERKLE
 Statistics, Normal Distribution, data points, PROBLEM NO.

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