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Unformatted text preview: e the level of significance. (There are z and z2 in p0 (1 p0 ) / n the following table because the central limit theorem is applied.)
Test H0 H1 Lefttailed p p0
or p p0 p p0 Righttailed p p0
or p p0 p p 0 Twotailed p p0 Reject H0 if and only if p p0 2 p p0
ˆ z
p0 (1 p0 ) / n
p p0
ˆ z
p0 (1 p0 ) / n p p0
ˆ
p0 (1 p0 ) / n z2 Questions
I. Inference about a Population Mean when variance is known
1. A car has an average fuel consumption of 33 mpg (with σ = 5.7). We took the new model of the car out for 35 tests
and collected the following data, x = 34.8 mpg. Does this new model have better fuel consumption than the original
¯
one? Assume the new model has the same σ , do a hypothesis test at 5% signiﬁcance level.
2. A manufacturer has produced a large batch of fanbelts. From past experience he knows that his machine capability
is σ = 0.7 cm which represents the standard deviation of fanbelt lengths in any large batch produced. To estimate
the mean length (µ cm) of the batch, the manufacturer randomly selected 20 items and obtained these measurements
(in cm):
52.5, 53.0, 52.3, 52.4, 52.7, 51.7, 52.1, 52.8, 53.1, 54.0,
52.9, 52.3, 51.6, 52.7, 52.6, 53.0, 52.3, 52.1, 51.7, 53.0
(a) Determine a 90% conﬁdence interval for µ.
(b) Test the null hypothesis H0 : µ = 52.0 versus the alternative H0 : µ ...
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This note was uploaded on 08/26/2013 for the course STAT 0302 taught by Professor Guo during the Spring '12 term at HKU.
 Spring '12
 guo
 Statistics, Variance

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