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You can tweak all the options and settings in the PowerShot G11 s menus and save those settings as a group of custom settings, designated 1 and 2. When you nd that you have favorite settings for shooting portraits or landscapes and you want to retain them for later use, assign them to a custom setting. To overwrite, you simply create a new collection of settings and save them to a previous C1 or C2 setting.

14. Suppose that the sixes in the Purple cipher consist of the vowels, AEIOUY. What is the expected frequency of each of the sixes and what is the expected frequency of each of the twenties Suppose instead that the sixes consist of JKQVXZ. What is the expected frequency of each of the sixes and what is the expected frequency of each of the twenties To answer these questions, use the English letter frequency distribution given in Table 1.3 in 1.

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We may also nd a P-value for the F-statistic in Example 10-11. Since f0.50,19,19 1.00, the computed value of the test statistic f0 s 2 s 2 3.84 4.54 0.85 is nearer the lower 1 2 tail of the F distribution than the upper tail. The probability that an F-random variable with 19 numerator and denominator degrees of freedom is less than 0.85 is 0.3634. Since it is arbitrary which population is identi ed as one, we could have computed the test statistic as f0 4.54 3.84 1.18. The probability that an F-random variable with 19 numerator and denominator degrees of freedom exceeds 1.18 is 0.3610. Therefore, the P-value for the test statistic f0 0.85 is the sum of these two probabilities, or P 0.3634 0.3610 0.7244. 2 Since the P-value exceeds 0.05, the null hypothesis H0: 2 1 2 cannot be rejected. (The probabilities given above were computed using a hand-held calculator.)

10-5.4

15. Consider the Purple cipher. For each of the = 217.8 choices for the sixes, let E6 be the average frequency for each of the sixes letters and

Appendix Charts VIo, VIp, VIq, and VIr provide operating characteristic curves for the F-test given in Section 10-5.1 for 0.05 and 0.01, assuming that n1 n2 n. Charts VIo and VIp are used with the two-sided alternate hypothesis. They plot against the abscissa parameter

(10-30)

for various n1 EXAMPLE 10-12

the let Ezo be the average frequency for each of the corresponding twenties letters. For how many of these 217.8 selections is - E 0 < 0.1 21 To answer this question, use the English letter frequency distribution in Table 1.3 in 1.

For the semiconductor wafer oxide etching problem in Example 10-11, suppose that one gas resulted in a standard deviation of oxide thickness that is half the standard deviation of oxide thickness of the other gas. If we wish to detect such a situation with probability at least 0.80, is the sample size n1 n2 20 adequate Note that if one standard deviation is half the other,

By referring to Appendix Chart VIo with n1 n2 n 20 and 2, we nd that 0.20. Therefore, if 0.20, the power of the test (which is the probability that the difference in standard deviations will be detected by the test) is 0.80, and we conclude that the sample sizes n1 n2 20 are adequate.

16. Suppose that we have two ciphers, both of which encrypt elements of { 0 , 1 , 2 , .. . ,7} using permutations, where the permutation varies with each step. One of these, known as cipher A , is a rotor machine, analogous to the Enigma, while the other, known as cipher B , is a switch-based machine, analogous to Purple. Which of the permutations P,Q, . . . , W , below, could have been generated by the A cipher and which could have been generated by the B cipher In each case, justify your answer.

10-5.5

2 1 2 2,

2.11 The Save Settings menu. You can create custom settings and save them as a group to the C1 and C1 modes.

2 2 2 1

0 5 3 7 1 3 2 7 6

is an F with n2 1 and n1 1 degrees of freedom. Therefore, P1 f1 2, n2 1, n1 1 F f 2,n2 1, n1 1 2 1 . Substitution for F and manipulation of the inequalities will lead to the 100(1 )% con dence interval for 2 2. 1 2

De nition If s2 and s2 are the sample variances of random samples of sizes n1 and n2, respec1 2 2 tively, from two independent normal populations with unknown variances 2 and 2 , 1 2 2 then a 100(1 )% con dence interval on the ratio 1 2 is s2 1 f s2 1 2

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