posted by Mary .
Inferences about Two Proportions technique (Chapter 9):
There is a claim that proportion of successes increased in 2009 compare to 2008.
For data given in Table 1
Number of cases Number of successes
2008 400 180
2009 500 235
Calculate pooled sample proportion and z-test statistics
Use a significance level of á = 0.05 to make decision if there is a considerable change of proportion of successes.
This would fit a one-tailed proportional z-test (using proportions). The test would be one-tailed because of the alternate hypothesis (p2009 > p2008).
Here is one formula:
z = (p2009 - p2008)/√[pq(1/n1 + 1/n2)]
...where 'n' is the sample sizes, 'p' is (x1 + x2)/(n1 + n2), and 'q' is 1-p.
I'll get you started:
p = (180 + 235)/(400 + 500) = ? -->once you have the fraction, convert to a decimal (decimals are easier to use in the formula).
q = 1 - p
p2008 = 180/400
p2009 = 235/500
Convert all fractions to decimals. Plug those decimal values into the formula and find z. Once you have this value, compare to the critical value from a z-table using 0.05 significance for a one-tailed test.
If the test statistic exceeds the critical value from the table, reject the null and accept the alternate hypothesis (p2009 < p2008). If the test statistic does not exceed the critical value from the table, then you cannot reject the null and you cannot conclude a difference.
I hope this will help.