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. Nationally, 40 percent of children under 5 who received antibiotics did not have a throat swab. The Colorado Department of Health took a random sample of 76 children under the age of 5 who received antibiotics for throat infections and found that 24 did not have a throat swab. At α = .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.

a. H₀: π ≥ .40 vs. H₁: π < .40

b. H₀: π ≤ .40 vs. H₁: π > .40

c. H₀: π = .40 vs. H₁: π ≠ .40

(a-2) Calculate the critical value. (A negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)
     

(a-3) Calculate the test statistic. (A negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
  

(a-4) Interpret the results:(choose one)

a. Fail to reject H₀

b. Reject H₀

(b) Is it safe to assume normality of the sample proportion p?

a. Yes, normality is justified.

b. No, normality is not justified.

Answer 1

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