august 3, 2018 What do you think would have happened if we had time to do the same activity but with a sample size of 10?

Transcription

1 august 3, 2018 summary from yesterday! What do you think would have happened if we had time to do the same activity but with a sample size of 10? Increasing the sample size decreases the variability of the sampling distribution. What does one of the blue dots represent? A sample of 5 words, and an average calculated from that sample. Aug 2 4:00 PM

2 What is the difference between a population and a sample? Population the entire group of individuals under the study Sample part of the population actually examined in order to gather information Parameter a number that describes some characteristic of the population (the value of the parameter is usually unknown because we cannot examine the entire population.) Statistic a number that describes some characteristic of a sample (we use a statistic to estimate an unknown parameter)

3 ways to collect data attempt to contact every individual in the entire population 1. Census study a part to gain information about the whole 2. Sampling EXAMPLE: The student government at a high school surveys 100 of the students at the school to get their opinions about a change to the bell schedule. Identify the population and sample. The population is all the students at school. The sample is the 100 students surveyed.

4 BIAS systematically favors certain outcomes people choose 1. interviewers choose 2. personal choice always produces bias (gender, race, age, religion) Badly Designed Sampling Methods people who choose themselves by responding to a general appeal. * people with strong opionions are most likely to respond. * some also allow volunteers to respond more than once! 1. Voluntary response internet survey, opinion polls, call in TV shows (American Idol) Ex. chooses individuals easiest to reach 2. Convenience sampling **AP EXAM TIP: If you re asked to describe how the design of a study leads to bias, you re expected to identify the direction of the bias i.e. the method leads to an overestimate or underestimate of the population proportion. EXAMPLE: To estimate the proportion of families that oppose budget cuts to the athletic department, the principal surveys families as they enter the football stadium on Friday night. Explain how this plan will result in bias and how the bias will affect the estimated proportion. This design is biased since it systematically favors a "no" outcome. If the principal were to conduct a similar survey over and over again, each time the result will probability overestimate the proportion of people who would respond "no."

5 Check your Understanding For each situation, identify the sampling method used. Then explain how the sampling method could lead to bias. 1. A farmer brings a juice company several crates of oranges each week. A company inspector looks at 10 oranges from the top of each crate before deciding whether to buy all the oranges. Convenience sampling. This could lead him to think that the oranges are of better quality than they really are, if the farmer puts the best oranges on top! 2. The ABC program Nightline once asked whether the United Nations should continue to have its headquarters in the United States. Viewers were invited to call one telephone number to respond Yes and another phone for No. There was a charge for calling either number. More than 186,000 callers responded, and 67% said No. Voluntary Response Sampling. Only those who feel particularly strongly about the issue are likely to respond. In this case, those who are happy that the United Nations has its headquarters in the United States already have what they want and so are less leikely to worry about responding to the question.

6 1. Simple Random Sample (SRS): Sampling Methods (We will do more sampling methods on Monday!) n individuals from the population are chosen in such a way that every set of n individuals has an equal chance to be in the sample actually selected. Ways to choose a SRS: Drawing names of the whole population from a hat Random Number Generator on the Calculator Table of Random Digits

7 Table of Random Digits EXAMPLE: Mall Hours The management company of a local mall plans to survey a random sample of 3 stores to determine the hours they would like to stay open during the holiday season. Use Table D at line 101 to select an SRS of size 3 stores. Describe your method that you used and then identify the stores that have been chosen.

8 HOMEWORK page 226 (1, 3, 7, 8, 9, 11, 13, 17)