Settlers often chose sites to live and build communities in based on the landscape's defensibility. The defensibility of archaeological sites in the Northwest Pacific was investigated in the Journal of Anthropological Archaeology (Vol. 35, 2014). A defensibility index was calculated for each in a sample of 23 sites that included a trench embankment. These index values (on a scale of 1 to 100) are listed in the accompanying table. The researcher determined that the mean defensibility index of the entire Northwest Pacific landscape is 47. Of interest is whether the defensibility index of a sampled site exceeds this mean.

a. Estimate p, the true proportion of all trench embankment sites that have a defensibility index that exceeds the mean of the entire Northwest Pacific landscape.
SAS Output for Exercise 8.90,

b. An archaeologist wants to conduct a statistical test of hypothesis to determine if p is larger than .60. Give the null and alternative hypotheses for this test.
c. Demonstrate that the sample is not large enough to apply the large-sample test of a binomial proportion.
d. The SAS printout shown on p. 407 gives the results of an exact binomial proportion test of the hypotheses, part b. Locate the p-value of the test (bottom of the printout) and interpret the results.

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70 68 55 70 55 67 66 65 67 51 52 52 63 59 57 46 44 37 57 63 46 70 57 54 The FREQ Procedure Cumulative Cumulative Frequency Percent Frequency Percent х ABOVE 19 82.61 19 82.61 BELOW 17.39 23 100.00 Binomial Proportion x = ABOVE Proportion (P) 0.8261 ASE 0.0790 95% Lower Conf Limit 0.6712 95% Upper Conf Limit 0.9810 Exact Conf Limits 95% Lower Conf Limit 0.6122 95% Upper Conf Limit 0.9505 Test of HO: Proportion = 0.6 A SE under HO 0.1022 2.2133 One-sided Pr > Z 0.0134 Two-sided Pr > IZI 0.0269 Exact Test One-sided Pr >= P 0.0190 Two-sided - 2* One-sided 0.0379 Sample Size - 23