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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
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 รก = 0.05 to make decision if there is a considerable change of proportion of successes.

  • STATS -

    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.

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