The data for the 10,000 simulated dog€“owner matches shown in Figure 4.7 on page 237 are given in Table 4.6. We are testing H₀: p = 0.5 (random guessing) vs H_a: p > 0.5 (evidence of a dog€“owner resemblance).

Figure 4.7

Table 4.6

(a) Use the data in the table to verify that the p-value for the observed statistic of 16 correct matches is 0.1145.
(b) Use the data to calculate a p-value for an observed statistic of 20 correct matches.
(c) Use the data to calculate a p-value for an observed statistic of 14 correct matches.
(d) Which of the three p-values in parts (a) to (c) gives the strongest evidence against H₀?
(e) If any of the p-values in parts (a) to (c) indicate statistical significance, which one would it be?

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1600 1400 1200 16 1000 800 1145 600 - 10,000 400 200 4 5 6 7 8 9 1011 121314 151617 18192021 Matches Frequency Correct matches Frequency Correct matches Frequency 12 5 17 4 10 54 341 972 11 1302 148 599 1549 14 19 13 15 16 612 17 322 18 142 20 1344 21 4 1551 977 51 14