Worked solution P55-Easy-1. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-2. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-3. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-4. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-5. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-6. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-7. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-8. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-9. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-10. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-11. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-12. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-13. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-14. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-15. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-16. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-17. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-18. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Easy-19. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-1. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-2. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-3. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-4. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-5. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-6. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-7. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-8. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-9. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-10. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-11. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-12. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-13. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-14. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-15. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-16. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-17. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-18. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Tough-19. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-1. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-2. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-3. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-4. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-5. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-6. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-7. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-8. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-9. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-10. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-11. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-12. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-13. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-14. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-15. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-16. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-17. The required sample size is 385, after rounding up. $$n=\frac{(1.96{)}^2(0.5)(0.5)}{(0.050{)}^2}=384.160\Rightarrow n=385.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-18. The required sample size is 461, after rounding up. $$n=\frac{(2.576{)}^2(0.5)(0.5)}{(0.060{)}^2}=460.818\Rightarrow n=461.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.

Worked solution P55-Toughest-19. The required sample size is 423, after rounding up. $$n=\frac{(1.645{)}^2(0.5)(0.5)}{(0.040{)}^2}=422.816\Rightarrow n=423.$$ Interpretation: Confidence describes the long-run success rate of the interval-producing method; the contextual interval estimates the named population parameter. Validity: The formula controls sampling margin only; design bias, nonresponse, and measurement error require separate planning. Error to reject: Never round a required sample size down, because doing so can exceed the stated margin.