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6.4 Select and Draw Conclusions

6.4 Select and Draw Conclusions. p. 230. Vocabulary. Population: group of people that you want information about. Vocabulary. Sample: part / subset of population Self-selected sample: people volunteer responses Systematic sample: rule selects members

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6.4 Select and Draw Conclusions

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  1. 6.4 Select and Draw Conclusions p. 230

  2. Vocabulary • Population: group of people that you want information about

  3. Vocabulary • Sample: part / subset of population • Self-selected sample: people volunteer responses • Systematic sample: rule selects members Ex: every other person • Convenience sample: easy-to-reach members • Random sample: every member has an equal chance of being selected

  4. Vocabulary • Unbiased sample: represents the population • Biased sample: over or underestimates the population

  5. EXAMPLE 1 Classify samples Baseball A sportswriter wants to survey college baseball coaches about whether they think wooden bats should be mandatory throughout college baseball. Identify the type of sample described if… • The sportswriter contacts only the coaches that he has cell phone numbers for in order to get quick responses. • The sportswriter mails out surveys to all the coaches and uses only the surveys that arereturned.

  6. EXAMPLE 1 Classify samples SOLUTION • The sportswriter selected coaches that are easily accessible. So, the sample is a convenience sample. • The coaches can choose whether or not to respond. So, the sample is a self-selected sample.

  7. SOLUTION The sample is biased because people standing in line for a rock concert are more likely to attend concerts than people in general. EXAMPLE 2 Identify a biased sample Concert Attendance The manager of a concert hall wants to know how often people in the community attend concerts. The manager asks 50 people standing in line for a rock concert how many concerts per year they attend. Tell whether the sample is biased or unbiased. Explain your reasoning.

  8. EXAMPLE 3 Choose an unbiased sample Senior Class Prom You are a member of the prom committee. You want to poll members of the senior class to find out where they want to hold the prom. There are 324 students in the senior class. Describe a method for selecting a random sample of 40 seniors to poll. SOLUTION Make: a list of all 324 seniors. Assign each senior a different integer from 1 to 324. STEP 1

  9. SOLUTION The students in one of his computer science classes were easy to reach. So, the sample is a convenience sample. The sample is biased as the students of only the computer class are surveyed. for Examples 1, 2, and 3 GUIDED PRACTICE • SCHOOL WEBSITE:A computer science teacher wants to know if students would like the morning announcements posted on the school’s website. He surveys students in one of his computer science classes. Identify the type of sample described, and tell whether the sample is biased.

  10. Margin of Error • How much it differs from population • smaller margin of error = more like population • = (where n is sample size) • To find range of possibility, take percent and then add/subtract your margin of error.

  11. In a survey of 1011 people, 52% said that television is their main source of news. EXAMPLE 4 Find a margin of error MEDIA SURVEY • What is the margin of error for the survey? • Give an interval (range) that is likely to contain the exact percent of all peoplewho use television as their main source of news.

  12. 1 = n = 0.031 + + + + – – – – 1 The margin of error for the survey is about 3.1%. ANSWER 1011 EXAMPLE 4 Find a margin of error SOLUTION • Use the margin of error formula. Margin of error Write margin of error formula. Substitute 1011for n. Use a calculator.

  13. It is likely that the exact percent of all people who use television as their main source of news is between 48.9% and 55.1%. ANSWER EXAMPLE 4 Find a margin of error • To find the interval, subtract and add 3.1% to the percent of people surveyed who said television is their main source of news (52%). 52% – 3.1% = 48.9% 52% + 3.1% = 55.1%

  14. 3. INTERNET: In a survey of 1202 people, 11% said that they use the Internet or e-mail more than 10 hours per week. What is the margin of error for the survey? How many people would need to be surveyed to reduce the margin of error to 2%? + – ANSWER + – 2500 people need to be surveyed. The margin of error for the survey is about 2.9%. for Examples 4 and 5 GUIDED PRACTICE

  15. D B A The correct answer is C. ANSWER C 1 n n n + + + + – – – – 1 = 0.05 1 = 0.05 Substitute for margin error. 0.0025 = EXAMPLE 5 Standardized Test Practice SOLUTION Use the margin of error formula. Margin of error Write margin of error formula. Square each side. n=400 Solve for n. There were 400 people surveyed.

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