To combat antibiotic resistance, the Quality Improvement Consortium recommends a
ID: 3311112 • Letter: T
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 83 children who received antibiotics for throat infections, 26 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.
Fail to reject H0
Reject H0
(b) Is it safe to assume normality of the sample proportion p?
No, normality is not justified.
Yes, normality is justified.
Explanation / Answer
A-1) Ho: >= 0.4 vs < 0.4
A-2) critical value is one sided z test value at 0.05%. Critical value= -1.645.
A-3) Test statistic z = { (26/83)-0.4 } / sqrt( 0.4*0.6/83)
Z = -1.614
A-4) fail to reject ho
B) yes, normality is justified, as sample size is large.
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