Essentials

APPENDIX B 245Chapter 21. (a) X 96.08, 2.7096.08 – 98.6z – 2.52 –4.672. 7 . 54 25This z is larger in magnitude than the critical value (1.96), so the result issignificant at the .05 level (two-tailed).–2.52(b) z –9.332.7 1 00(c)For .01, z crit 2.33 (one-tailed), or 2.58 (two-tailed). In either casethese results are significant at the .01 level. (Optional: Because thesample size was 4 times larger for part b than part a, the z-score wasmultiplied by 2 [i.e., the square root of 4].) x 2. 7; X z25crit x 96.08 1.96 (.54); so 96.08 1.06Therefore, the 95% CI goes from 95.02 to 97.14 (note that the sum ofthese two limits is 192.16, which is exactly twice as large as the samplemean, as will always be the case). Because the population mean tested inpart a (98.6) is not in this 95% CI, we know that the sample mean differssignificantly from this population mean at the .05 level.(d) x 2.71 ; 00X z crit x 96.08 2.58 (.27); so 96.08 .7Therefore, the 99% CI goes from 95.38 to 96.78.2. (a) X 6.5625(b) 4.873; x 4 .873 1.2261X z crit x 6.56 1.96 (1.22); so 6.56 2.39Therefore, the 95% CI goes from 4.17 to 8.95.(c) Yes, you can reject the null hypothesis at the.05 level (two-tailed) because9 is not contained in the 95% CI in part b.