To combat antibiotic resistance, the Quality Improvement Consortium recommends a

Question

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 59 children who received antibiotics for throat infections, 22 did not have a throat swab. At = 0.05, is this a statistically significant reduction over last year’s national rate of 40 percent? (a-1) Choose the correct null and alternative hypotheses. H0: 0.40 vs. H1: > 0.40 H0: = 0.40 vs. H1: 0.40 H0: 0.40 vs. H1: < 0.40 (a-2) Calculate the critical value. (A negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) Critical value (a-3) Calculate the test statistic. (A negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Test statistic (a-4) Interpret the results. Reject H0 Fail to reject H0 (b) Is it safe to assume normality of the sample proportion p? Yes, normality is justified. No, normality is not justified.

Explanation / Answer

(a) null and alternative hypotheses.

H0 : 0.40

Ha : < 0.40

(b) As it is one sided test, critical value = - 1.645

(c) Proportion of children who received anotibiotics p^ = 22/59 = 0.373

standard error of the proportion se0 = sqrt (p^ * (1-p^)/N) = sqrt [0.4 * 0.6/59] = 0.0638

Here,

Z = (p^ - 0.4)/se0  = (0.373 - 0.4)/ 0.0638 = -0.423

HEre Z > Zcritical in left sided test so we will not reject the null hypothesis.

Here it is safe to assume that normaity of sample proportions is justified as n > 30

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