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Chapter 12: Hypothesis Tests – Large Samples
Conclusion
: ……….
Note:
This is a two-tailed test because of the not-equal-to symbol in the
alternative hypothesis. Also, note that the level of significance is shared
equally when finding the critical
z
value (
).
Example 12-8:
A real estate agent, in trying to indicate the
“exclusiveness” of the restaurants in the area where he shows his clients real
estate properties, claims that the average meal price for a couple is $52. A
particular client feels otherwise. A sample of 64 meals for couples was
randomly selected and yielded a mean of $51.25 and a standard deviation of
$5. Test the client’s claim at the 5% level of significance.
Summary information
:
= 64,
= 5,
= 0.05,
̅
= 51.25,
=
=
1.96, and
= 52. Also,
√ ⁄
= 0.625.
Note the use of the sample estimate
s
of the population standard deviation
since
= 64
30.
This will be a two-tailed test since the client feels that the claim of the real
estate agent is not correct. Observe that whether the client feels that the
average price is less than $52 or more than $52 is not specified.
Solution:
52
52
:
̅
√ ⁄
= (51.25 – 52)/0.625 = - 1.20.
: For a significance level of
= 0.05, reject the null hypothesis if the
computed test statistic value
= -1.20 < -
= -1.96 or if
= -1.20 >
= 1.96. Alternatively, reject
if |-1.20| = 1.2 > 1.96.
Conclusion
:
Since | -1.2 | = 1.2 < 1.96, do not reject
. There is insufficient
sample evidence to refute the agent’s claim. The sample evidence does not