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On the basis of a one-tailed test at a level of significance of 0.05, we would reject the hypothesis H0 if the z score were greater than 1.645. We therefore cannot reject the hypothesis at this level of significance. It should be noted, however, that the hypothesis can be rejected at a level of 0.10 if we are willing to take the risk of being wrong with a probability of 0.10, i.e., 1 chance in 10. (b) The P value of the test is P(Z 1.32) 0.0934, which is the probability that the observed positive difference between mean heights of male athletes and other male students would occur by chance if H0 were true.

In the circuit of Fig. 9-55, v1 V1 cos 2t and v2 V2 cos 0:25t . Ans: vA 0:816V1 cos 2t 0:6V2 cos 0:25t

7.12. By how much should the sample size of each of the two groups in Problem 7.11 be increased in order that the observed difference of 0.7 inch in the mean heights be significant at the level of significance (a) 0.05, (b) 0.01

Suppose the sample size of each group is n and that the standard deviations for the two groups remain the same. Then under the hypothesis H0 we have mX1 X2 0 and sX1 s2 1 An s2 2 n (2.5)2 A n (2.8)2 14.09 A n 3.75 !n

10.1 POWER IN THE TIME DOMAIN The instantaneous power entering a two-terminal circuit N (Fig. 10-1) is de ned by p t v t i t 1

Risk ID: 1-010-77

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For an observed difference in mean heights of 0.7 inch, Z # # X1 X2 sX1 X2 0.7 3.75> !n 0.7 !n 3.75

where v t and i t are terminal voltage and current, respectively. If p is positive, energy is delivered to the circuit. If p is negative, energy is returned from the circuit to the source.

(a) The observed difference will be significant at a 0.05 level if 0.7 !n 3.75 1.645 or !n 8.8 or n 78 50 28.

Therefore, we must increase the sample size in each group by at least 78 (b) The observed difference will be significant at a 0.01 level if 0.7 !n 3.75 2.33 or !n 12.5 or n

Fig. 10-1

157 50 107.

In this chapter, we consider periodic currents and voltages, with emphasis on the sinusoidal steady state in linear RLC circuits. Since the storage capacity of an inductor or a capacitor is nite, these passive elements cannot continue receiving energy without returning it. Therefore, in the steady state and during each cycle, all of the energy received by an inductor or capacitor is returned. The energy received by a resistor is, however, dissipated in the form of thermal, mechanical, chemical, and/or electromagnetic energies. The net energy ow to a passive circuit during one cycle is, therefore, positive or zero.

7.13. Two groups, A and B, each consist of 100 people who have a disease. A serum is given to Group A but not to Group B (which is called the control group); otherwise, the two groups are treated identically. It is found that in Groups A and B, 75 and 65 people, respectively, recover from the disease. Test the hypothesis that the serum helps to cure the disease using a level of significance of (a) 0.01, (b) 0.05, (c) 0.10. (d) Find the P value of the test.

Description: Specialized hardware may not be available. Mitigation strategy: Build simulator, accelerate hardware development. Risk trigger: Hardware falling 1 week or more behind schedule. Contingency plan: Outsource hardware development as backup, deliver system on simulator. Status/date/responsible person: Created Jan 1,01 Fred Jones Sim. completed Feb 10, 01 Bill Olson

Let p1 and p2 denote, respectively, the population proportions cured by (1) using the serum, (2) not using the serum. We must decide between the two hypotheses H0: p1 H1: p1 p2, and observed differences are due to chance, i.e., the serum is ineffective p2, and the serum is effective

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