Unformatted text preview: e that the population mean is equal to 80. 3 0.025
79.216 0.025
80 X 80.784 reject reject 0.025 0.025 1.96
reject 0 1.96 Z
reject 4 2. A real estate expert claims the current mean value of houses in a particular
area is more than $250,000. A random sample of 150 recent sales prices in the
area yields a sample mean of $265,000. It is known that house values in the
area are approximately normally distributed with a standard deviation of
$50,000.
(a)Perform an upper tail test of the null hypothesis that the population mean
house value in the area is $250,000. Use a 5% level of significance and
state the rejection (critical) region in terms of both ̅ and z.
Let X value of a house in the area
̅
̅
We wish to test
Rejection region:
̅
⁄√
or
̅ ̅ ( √ √ ) Since ⁄√
Hence we reject H 0 and conclude that the mean house value in the area is
more than $250,000 .
(b) Why is an upper tail test most appropriate in this case? The nature of the research problem dictates an upper tail test. In this case we
will not believe the expert’s claim unless there is ‘significant’ sample evidence
to do so. This implies an upper tail test...
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 '11
 DenzilGFiebig
 Statistics, Statistical hypothesis testing, Type I and type II errors, α, upper tail test

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