Population size

* Population size doesn’t matter as long as…* Population > 10*n (10*sample size)

* As long as your sample is random, and your population is big enough, its size doesn’t matter to the variability of the statistic (the results).

Example

•There are two local high schools, Central High and North High. Central has 1,000 students and North has 3,500 students

•A researcher wants to determine the average income for the families that send their students to the different high schools.

•He has 2 different sampling methods:

•Sample 5% from each school

•Sample 100 students from each school

Try these:

• p. 234-235 #45 & 46

Margin of Error and Confidence Statements

Example:A newspaper article states that they took a poll of Americans and found that 65% of them think the President is doing a good job. They say that they are 95% confident about their results, but they have a margin of error of plus or minus3%.

What can you infer about the % of ALL Americans that think he’s doing a good job? Do you trust their results?

The same newspaper prints an article the next day saying that they were wrong, that they have a margin of error of 30%, not 3%. They are still 95% confident in their results though!

What can you infer about the % of ALL Americans that think the President is doing a good job?

The same newspaper prints another article. They took a new sample because their realized their margin of error was too high before. So now they have a margin of error of 5%. But they are only 60% confident in their results now.

What can you infer about the % of ALL Americans that think the President is doing a good job?

Margin of Error:

•Want it to be a low %

•Its always a plus or minus %

•Usually paired with a level of confidence

•Use both the level of confidence and the margin of error to decide whether you trust the results

•Larger samples mean lower margin of error.

Confidence Statement:

•Use both level of confidence, and margin of error, conclude about population•Example: 90% confident that 45% vote for Democrat, having a margin of error of 3%.

I am 90% confident that the true percent of the population that will vote for the Democrat is between 42% and 48%.

Try p. 232 #42 a &b, 43

42 (a) I am 95% confident that the true percent of the population that think Women had to give up too much to get better jobs is between 45% and 51%.

42 (b) Because 48% is just from the one sample (the one poll). Samples are not always representative of the population. This is why we need the margin of error

43) Men = 472 margin of error = 5%

Women = 1025 margin of error = 3%The margin of error for the men was larger because they had a smaller sample size. So their sample is more variable (wider histogram, less accurate).