7.SP.1 Random Sample. Created BY Melissa Forsyth

Transcription

1 7.SP.1 Random Sample Created BY Melissa Forsyth

2 Definitions Statistical questions are used to collect data about a population. Population: The entire group of objects or people being studied. Sample: Part of the population being surveyed. Example: How many texts do middle school students send in a day? Data: how many texts sent in a day Population: middle school students

3 How many texts do middle school students send in a day? Middle School Student Population To get your data you could ask every single student, but that would take a long time and would be impractical.

4 By surveying a sample of the population, you can make a generalization of the entire population.

5 Predict the winner of the upcoming election. Population: All American Voters Sample: Adults walking to work Generalization: We can then use the responses from the population to make a generalization and predict the winner of the election.

6 Tracking the migration pattern of a bird species. Population: Entire bird species Sample: Tagged birds Generalization: We can use the information gathered from the tagged birds to make generalizations about the bird species.

7 What is a random sample? In a random sample each member of the population has the same chance of being selected. Examples Names drawn out of a hat Rolling two 1s on a set of dice.

8 Bias When making generalizations about a population using a random sample we have to watch out for bias. Selection bias. This type of bias is introduced when some potential observations from the population are excluded from the sample by some systematic means. For example, if we were to carry out research on political information seeking by conducting in-house interviews, we might be tempted to systematically avoid those houses with Insured by Smith & Wesson signs, houses at the end of long muddy driveways, apartments on the fourth floor of rickety tenement buildings, and all the haunted-looking houses on Elm Street. By avoiding these places we would be selecting nice, reliable-looking houses, probably inhabited by nice, reliable people (like us, incidentally). As nice as this sample might be, it s probably not very representative of the population of voting citizens. If we try to generalize the conclusions of hypothesis tests from this sample to the whole population, we re probably going to be wrong. To be a bit formal, a sample contains selection bias whenever each unit in the population does not have an equal probability of being chosen for the sample. Sample bias can result from either the action of the scientist (selection bias) or from the units of the sample (response bias). The scientist must take steps to avoid both types of bias, so that the results of his study can be safely generalized to the population. The method of avoiding selection bias is quite simple: base the selection process on pure chance.

9 Random Sample or Not Jacob wanted to know what the most popular sneaker brand was of his classmates. His class had 30 students. To save time, he asked 10 boys the brand of sneakers that they were wearing. Of the students surveyed; Nike was the most popular sneaker brand. a) Survey girls as well. b)survey more students.

10 Random Sample or Not George put some cards into a basket. Then, he drew 3 cards out of the basket. Is this a random sample of the cards in the basket? Why or why not? In a random sample, every person or item has an equal chance of being chosen. Since every card had an equal chance being picked, in this case, it is a random sample.

11 What is a generalization? When the population is too large or too difficult to poll in its entirety, polling a random sample can help us to better predict what will happen with the entire population. We can use our knowledge of percentages, mean, median, and mode to make predictions about populations.

12 Making Generalizations A counselor surveys a random sample of 60 out of 900 high school students. 75% of them said they were going to college. She used these results to determine that 675 students in the overall school would be planning to go to college. Do you agree with her prediction? If the counselor s sample was random you can use the percentage of students whom said they would attend college to predict the number of total students at the high school whom will attend college. 75% 100 = x number of students going to college 900 total students at high school Cross multiply and solve for x. 100x = x = x = 675 students going to college.

13 Making Generalizations A survey asked 72 randomly chosen students if they were going to attend the school play. Twelve said yes. If there are 210 tickets sold for the play, predict the number of students who attend the school. 12 going to play 72 random students = % % of students going to play 100 = 210 students at play x total amount of students Cross multiply and solve for x x = x = x = 1260 total students

14 Making Generalizations A survey asks 48 randomly chosen students if they plan to buy a school newspaper this week. Of the 48 surveyed, 32 plan to buy a school newspaper. If 360 students bought papers, predict the number of students enrolled at the school. 32 going to buy newspaper 48 random students = % % of students going to buy newspaper 100 = 360 buy newspapers x total amount of students Cross multiply and solve for x x = x = x = 540 total students

15 Making Generalizations The following data set represents survey results on a scale of 1 to 10. {4, 5, 7, 6, 4, 4, 5, 4, 6, 5} Based on this data set, which of the following responses would be most likely given by the next person surveyed? Looking at the data we can see there is clearly a mode, a number given the most. The mode of this set of numbers is 4. This means that 4 may be more likely to be chosen by the next person.

16 Making generalizations The following data set represents survey results on a scale of 1 to 10. {7, 7, 8, 7, 9, 8, 8, 8, 7, 7, 9} Which of the following survey result would you be most surprised with if given by the next person surveyed? 4 would be the biggest surprise because the results are all 7 or above.