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IV is correct I Let m = the true mean score for all students taking the exam H0: m = 520 (or, H0: m 520) HA: m > 520 II We will use a one-sample t-test We consider the 175 students to be a random sample of students taking the exam The sample size is large, so the conditions for inference are present (Note: Due to the large sample size, it is reasonable that the sample standard deviation is a good estimate of the population standard deviation This means that you would receive credit on the AP exam for doing this problem as a z-test although a t-test is preferable) 96 531 520 = 726 t = III x = 531, s = 96, s x = = 152 , 96 175 175 df = 175 1 = 174 005 < P-value < 010 (from Table B, with df = 100 always round down) (Using the TI-83/84, P-value = tcdf(152,100,174)=0065 If we had used s = 96 as an estimate of based on a large sample size, and used a z-test rather than a t-test, the P-value would have been 0064 This is very close to the P-value determined using t Remember that is a t-test but that the numerical outcome using a z-test is almost identical for large samples) IV The P-value, which is greater than 005, is reasonably low but not low enough to provide strong evidence that the current class is superior in math ability as measured by the SAT

Species can also be categorized in the ways in which they adapt to their environment The first, known as r-adapted species, produce lots of offspring and have a high rate of growth (rN) These opportunistic species are generally lower on the food web and use great numbers of offspring to ensure species survival Weeds, such as dandelions, which spread almost overnight in a lawn, fit into this category Long-lived species, which produce slower maturing and fewer offspring, like elephants (eg, reaching reproductive maturity around age 20 and giving birth only every 4 to 5 years), maintain a generally stable population with the carrying capacity (K) of their environment Elephants, then, are called K-adapted species, and tend to live 60 to 70 years if not heavily impacted by density-independent factors such as habitat loss or heavy poaching Adaptation strategies are detailed in Table 111

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Rapid growth Early maturity Numerous offspring Short life Little to no parental nurturing or protection Adaptation to varied environment Pioneers, colonizers Niche generalists Prey Affected by internal factors Low on food web

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5 I Let m = the true average number of pages in the books Booker reads H0: m 375 HA: m > 375 II We are going to use a one-sample t-test test at = 005 The problem states that the sample is a random sample A dotplot of the data shows good symmetry and no significant departures from normality (although the data do spread out quite a bit from the mean, there are no outliers):

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