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Chapter 12: Hypothesis Tests – Large Samples
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Summary information
:
Let
be the proportion of the 18 – 24 age group
without health insurance. Let
be the proportion of the 35 – 44 age group
without health insurance. From the information given,
= 75,
= 100,
̂
=
= 0.6667,
̂
=
= 0.45,
̂
=
=
= 0.5429,
= 0.01,
⁄
=
= 2.576.
Solution:
:
(
)
:
(
)
̂
̂
√ ̂ ̂ (
)
√
= 2.8517
D.R:
For a significance level
= 0.01, reject the null hypothesis if | 2.8517 |
= 2.8517 >
= 2.576.
Conclusion
:
Since 2.8517 > 2.576, reject
. There is sufficient sample
evidence to conclude that the proportion of those without health insurance
was significantly different between the 18 – 24 age group and the 35 – 44
age group, at the 1% level of significance.
Note:
There is a significant difference between the difference between the
sample proportions and the postulated value of 0.
Figure 12-23
displays the test statistic in relation to the rejection region.
Observe that the test statistic falls in the rejection region.