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 100 children under the age of 5 who received antibiotics for throat infections and found that 30 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. H0: π ≥ .40 vs. H1: π < .40 H0: π ≤ .40 vs. H1: π > .40 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.) 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.
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 100 children under the age of 5 who received antibiotics for throat infections and found that 30 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.
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H0: π ≥ .40 vs. H1: π < .40
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H0: π ≤ .40 vs. H1: π > .40
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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.)
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.
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Reject H0
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Fail to reject H0
(b) Is it safe to assume normality of the sample proportion p?
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Yes, normality is justified.
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No, normality is not justified.
rev: 10_08_2019_QC_CS-185060
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