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 59 children under the age of 5 who received antibiotics for throat infections and found that 22 did not have a throat swab. At = .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: .40 vs.H₁:< .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 rejectH₀

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

Yes, normality is justified.