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GROUP 5: describe evidence of evolution such as homology, DNA/protein sequences, plate tectonics, fossil record, embryology, and artificial selection/agriculture, explain how populations of organisms have changed over time showing patterns of descent with modification from common ancestors to produce the organismal diversity observed today, describe how the present system of classification of organisms is based on evolutionary relationships

Lesson 1: Evidence of Evolution

Several lines of evidence support the theory of evolution. Homology refers to similarities in structures among different species that suggest a common ancestry, such as the forelimbs of humans, cats, whales, and bats, which have different functions but share the same basic bone arrangement. DNA and protein sequences also provide strong evidence, as closely related species share a high percentage of genetic material, while differences accumulate over time due to mutations. Plate tectonics helps explain the distribution of organisms, as continental drift separated populations and led to the development of unique species on different landmasses. The fossil record reveals how organisms have changed over millions. of years, showing transitional forms such as Archaeopteryx, which shares features of both dinosaurs and birds. Embryology. shows that embryos of vertebrates pass through similar developmental stages, suggesting a shared ancestry. Artificial selection in agriculture and domestication demonstrates how humans can drive evolutionary change by selecting traits, providing a model for how natural selection operates in nature.

Lesson 2: Patterns of Descent with Modification

Evolution explains how populations of organisms change over time, giving rise to the diversity of life seen today. Populations adapt to their environment through natural selection, where advantageous traits increase in frequency because they improve survival and reproduction. Over long periods, these changes accumulate, leading to new species. Descent with modification means that all organisms share common ancestors, but each lineage has undergone changes that reflect adaptation to different environments. For example, finches in the Galápagos Islands evolved different beak shapes depending on the types of food available. Similarly, whales descended from land-dwelling mammals, gradually adapting to aquatic life. These patterns demonstrate how biodiversity arises not from sudden appearance, but from gradual divergence of lineages through evolutionary processes.

Lesson 3: Classification and Evolutionary Relationships

The present system of classifying organisms is based on evolutionary relationships rather than just physical similarities. Early classification systems, such as those by Linnaeus, grouped organisms mainly by observable traits. Today, modern taxonomy and systematics use phylogenetics, which relies on DNA sequences, molecular evidence, and evolutionary history to determine relationships. Organisms

1. Estimation

2. Estimation is an area of Inferential Statistics concerned with trying to determine the true value of the population parameters. Estimator – any statistic whose value is used to estimate an unknown parameter. The realized value of an estimator is the estimate .

3. Point estimate – is a single value used to represent the parameter of interest. Interval estimate – is a rule that tells us how to calculate two numbers based on a sample date, forming an interval within which the parameter is expected to lie. (a, b) – interval estimate or confidence interval. The degree of certainty attached to an interval estimate for the unknown parameter is , called the level of confidence or confidence coefficient   Estimation

4. Point Estimation of the Mean, Standard Deviation and Proportion Statistics are used to estimate the parameters Parameter Statistic Population Mean, Population Standard Deviation, Population Proportion, p Parameter Statistic Population Proportion, p

5. Examples The number of incorrect answers on a true or false test for a sample of 15 students were recorded as follows: 2, 1, 3, 0, 1, 3, 6, 0, 3, 3, 5, 2, 1, 4, 2. Find a good point estimate each for the mean, standard deviation and variance. In a certain class 5 out of 45 students are left-handed. Estimate the proportion of left-handed students.

6. Confidence interval for , is known If is the mean of a random sample from a population with known variance, a level of confidence interval is given by where   Interval Estimation of the Mean of a Single Population

7. Interval Estimation of the Mean of a Single Population Confidence Level

8. Examples A survey of the delivery time of 100 orders worth P20,000 from Green Cab yielded a mean of 55 minutes with a standard deviation of 12 minutes. Assuming that the delivery time follows a normal distribution, construct a. 95% confidence interval for the true mean. b. 99% confidence interval for the true mean.

9. Examples A survey of the delivery time of 100 orders worth P20,000 from Green Cab yielded a mean of 55 minutes with a standard deviation of 12 minutes. Assuming that the delivery time follows a normal distribution, construct a. 95% confidence interval for the true mean.  

10. Examples  

11. Examples A survey of the delivery time of 100 orders worth P20,000 from Green Cab yielded a mean of 55 minutes with a standard deviation of 12 minutes. Assuming that the delivery time follows a normal distribution, construct b. 99% confidence interval for the true mean.  

12. Interval Estimation of the Mean of a Single Population Confidence Level

13. Examples A survey of the delivery time of 100 orders worth P20,000 from Green Cab yielded a mean of 55 minutes with a standard deviation of 12 minutes. Assuming that the delivery time follows a normal distribution, construct b. 99% confidence interval for the true mean.  

14. Examples  

15. Confidence interval for , is unknown If and are the mean and SD respectively, of a random sample from a population with unknown variance, a level of confidence interval is given by where t-value with .   Interval Estimation of the Mean of a Single Population

16. Examples Compute the 95% confidence interval estimate of given the following It can be deduced that Using the table, at confidence level and  

17. Examples Compute the 95% confidence interval estimate of given the following It can be deduced that Using the table, at confidence level and  

18. Examples  

19. Examples The contents of 7 similar containers of sulfuric acid are 9.8, 10.2, 10.4, 9.8, 10.0, 10.2 and 9.6 liters. Find a 95% confidence interval for the mean content of all such containers, assuming an approximate normal distribution for containers contents.  

20. Examples The contents of 7 similar containers of sulfuric acid are 9.8, 10.2, 10.4, 9.8, 10.0, 10.2 and 9.6 liters. Find a 95% confidence interval for the mean content of all such containers, assuming an approximate normal distribution for containers contents.  

21. Examples  

22. ACTIVITY

23. REVIEW The scores of some students who took a quiz are as follow: 11, 10, 11, 12, 8. Construct a 90% confidence interval of the true mean.  

24. Error and Sample Size in Estimating the Population Mean Error is computed by while sample size is  

25. Examples A random sample of 100 PUJ shows that a jeepney is driven on the average 24,500 km/year, with a standard deviation of 3,900 kms . What can we assert with 99% confidence about the possible size of our error if we estimate the average number of km. driven by jeepney drivers to be 24,500 km/year?  

26. Examples  

27. Examples In a study of physical attractiveness and mental disorders 231 subjects were rated for attractiveness, a the resulting mean and standard deviation are 3.94 and 0.75 respectively. Determine the sample size necessary to estimate the sample mean, assuming you want a 95% confidence interval and a margin of error of 0.05.  

28. Examples  

29. Interval Estimation of the Population Proportion If and are the mean and SD respectively, a level of confidence interval is given by where:  

30. Examples In a survey, 1000 Grade 7 students were asked if they read storybooks. There were 318 who said yes. What proportion of the students does not read storybooks? Use 95% confidence interval to determine the proportion of all Grade 7 students who read storybooks.

31. Examples In a survey, 1000 Grade 7 students were asked if they read storybooks. There were 318 who said yes. What proportion of the students does not read storybooks? Let be the proportion of students who read storybooks. Let be the proportion of students who does not read storybooks.  

32. Examples In a survey, 1000 Grade 7 students were asked if they read storybooks. There were 318 who said yes. b. Use 95% confidence interval to determine the proportion of all Grade 7 students who read storybooks.  

33. Examples  

34. Examples An interval estimate , called a confidence interval , is a range of values that is used to estimate a parameter. This estimate may or may not contain the true parameter value. The confidence level of an interval estimate of a parameter is the probability that the interval estimate contains the parameter. It describes what percentage of intervals from many different samples contain the unknown population parameter

35.   Say you were interested in the mean weight of 10-year-old girls living in the United States. Since it would have been impractical to weigh all the 10-year-old girls in the United States, you took a sample of 16 and found that the mean weight was 90 pounds. This  sample  mean of 90 is a  point estimate  of the  population  mean. A point estimate by itself is of limited usefulness because it does not reveal the uncertainty associated with the estimate; you do not have a good sense of how far this sample mean may be from the population mean. For example, can you be confident that the population mean is within 5 pounds of 90? You simply do not know. Confidence intervals provide more information than point estimates. Confidence intervals for means are intervals constructed using a procedure (presented in the  next section ) that will contain the population mean a specified proportion of the time, typically either 95% or 99% of the time. These intervals are referred to as 95% and 99% confidence intervals respectively. An example of a 95% confidence interval is shown below: 72.85 < μ < 107.15