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 a = .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. O Ho: T.40 vs. H: 17 < .40 O Ho: TTS.40 vs. H: T> .40 O Ho: T = .40 vs. H: 1 ± .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. O Fail to reject Ho O Reject Ho

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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 = 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.**

- \( H_0: \pi \geq .40 \) vs. \( H_1: \pi < .40 \)
- \( H_0: \pi \leq .40 \) vs. \( H_1: \pi > .40 \)
- \( H_0: \pi = .40 \) vs. \( H_1: \pi \neq .40 \)

**(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: [Input]

**(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: [Input]

**(a-4) Interpret the results.**

- Fail to reject \( H_0 \)
- Reject \( H_0 \)

Please fill in the blanks with the appropriate calculations and interpretations based on your analysis.
Transcribed Image Text: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 = 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.** - \( H_0: \pi \geq .40 \) vs. \( H_1: \pi < .40 \) - \( H_0: \pi \leq .40 \) vs. \( H_1: \pi > .40 \) - \( H_0: \pi = .40 \) vs. \( H_1: \pi \neq .40 \) **(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: [Input] **(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: [Input] **(a-4) Interpret the results.** - Fail to reject \( H_0 \) - Reject \( H_0 \) Please fill in the blanks with the appropriate calculations and interpretations based on your analysis.
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