To combat antibiotic resistance the Quality Improvement Cons

To combat antibiotic resistance, the Quality Improvement Consortium recommends a throat swab to confirm strep throat before a physician prescribes antibiotics to children under age 5. In a random sample of 83 children who received antibiotics for throat infections, 23 did not have a throat swab. At ? = 0.05, is this a statistically significant reduction over last year

Solution

It is a left-tailed test.

Given a=0.05, the critical value is Z(0.05) =-1.645 (from standard normal table)

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The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(23/83-0.4)/sqrt(0.4*0.6/83)

=-2.29