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Chapter 12: Hypothesis Tests – Large Samples
Conclusion
:
Since 0.0000 < 0.05, reject
. There is sufficient sample
evidence to conclude that the average score using Method A is less than the
average score using Method B, at the 5% level of significance.
Note:
There is a significant difference for the difference between the
sample means of 74 – 83 = -9 and the postulated value of 0.
(c) Two-tailed
:
:
̅
̅
√
or
̅
̅
√
for
30 and
30
: For a specified significance level
, reject the null hypothesis if
the computed test statistic value
or if
(this is
equivalent to
| |
).
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 12-15:
Arandom sample of size
=36 selected from a normal
distribution with standard deviation
= 14 has a mean
̅
= 75. A second
random sample of size
= 25 selected from a different normal distribution
with standard deviation
= 16 has a mean
̅
= 85. Is there a significant
difference between the population means at the 1% level of significance?
Solution:
:
(
= 0)
:
(
0)