550 / 762
550
Chapter 12: Hypothesis Tests – Large Samples
:
p
1
>
p
2
(
p
1
-
p
2
> 0)
: z =
̂
̂
√
=
√
= 2.7621
: For a significance level
= 0.05, reject the null hypothesis if the
computed test statistic value
= 2.7621 >
= 1.645.
Conclusion
:
Since 2.7621 > 1.645, reject
. There is sufficient sample
evidence to conclude that the proportion of smokers in 2010 was greater
than the proportion of smokers in 2012 at the 5% level of significance.
Note:
There is a statistical significant difference between the difference
between the sample proportions of 0.51 – 0.38 = 0.13 and the postulated
value of 0 for the population proportions.
Figure 12-20
displays the test statistic in relation to the rejection region.
Observe that the test statistic falls in the rejection region.