Take Home Quiz and Study; updated Saturday with an explanation of parameters v. statistics...

You have two responsibilities this weekend...

1.) Complete the chapter 18 take home quiz provided in class (or below). You MUST SHOW WORK for questions 2, 3, 7, 8, and 11 or you will not receive credit! I expect you to work hard and use your resources to figure this out! We will be starting new stuff on Monday, no exceptions! Step up to the challenge and make yourself (and me) proud!

2.) Study! We will start class on MONDAY with our CHAPTER 18 VOCAB QUIZ! (List below).

• We did not cover all of the terms in class! Use the definitions below! Even if you were out, you're taking this quiz--so study, study, study! No excuses!

Here are some hints/info about your take home quiz (by question)!

I also recommend the 4 videos the AP Stats Guy has! (Link on the right; they are videos 1-4 under Unit 5!)

1. Read carefully here! Use your notes about parameters and statistics, or maybe even check some definitions on page 287 of your textbook!
2. This question asks about the "mean number of admissions"--since it's about the "mean of a sample," we'll have to use a sampling distribution! Take a look at the key provided in class today for last night's homework for a sample problem, or look at the "step by step" example on pages 423-424 in your book! (if you don't have the key I provided today, you can also take a look at the 2010 AP Scoring rubric online, linked in yesterday's post below).
3. Here, we have a sampling distribution for proportions, b/c the question is asking us about a "% of a sample!" This is based on the ideas/math we discussed today in class....or, check out the "step by step" example on pages 415-416!
4. Think about what type of data we are collecting, then check your notes--we discussed when we use each type of sampling distribution depending on the type of data we collect!
5. See #4's hint.
6. You might look back at the table we created in our notes with the correct symbols for statistics/parameters from chapter 12! Or, you can find this table on p. 276 of your book!
7. Back to the sampling distribution for proportions...take a look at the table we created in our notes (Thursday) for the correct mean/standard deviation formulas! 
8. See #3's hint.
9. This deals with an idea called the "Law of Diminishing Returns" that we may or may not have discussed today in class. Either way, you can find more about this on page 423 of your book!
• It comes down to this concept: if we quadruple our sample size (n x 4) we only cut the standard deviation in half (divide by 2) because of the square root in the formula! 
• Also, remember, if we increase sample size we will decrease standard deviation...
• If we take a smaller sample, we will increase standard deviation...
10. See #9's hint.
11. See #2's hint.

Chapter 18 Vocab List and Definitions:

• Sampling Distribution (a plot of sample statistics taken from repeated samples)
• Sampling Variability (the expected differences we see in sample statistics)
• Standard Error (an estimated standard deviation based on sample statistics)
• Central Limit Theorem (the sampling distribution for means is approximately Normal, and is more approximately Normal as the sample size increases)
• 10% Condition (our sample must be less than 10% of the entire population)
• "Large Enough Sample" Condition (we need a large sample unless the population is Normal)
• Conditions for a Sampling Distribution for Proportions (10%, random sample, np and nq>10)
• Conditions for a Sampling Distribution for Means (10%, random sample, large enough sample)
• Sampling Distribution for Means is use with quantitative data
• Sampling distribution for proportions is used with categorical data
• As n increases, standard deviation of a sampling distribution decreases
• Remember, a sampling distribution question will ask about the mean of a sample or the % of a sample...

I got an email question about understanding population parameters vs. sample statistics--check out the explanation! Not only will this help you with this weekend's work, but it is the guiding principle behind next week's topic, confidence intervals.

Population Parameters vs. Sample Statistics:

A population parameter refers to any number that summarizes an entire population; a population parameter may be a mean, for example, the average age of all of the people in the world. Or, it may be a proportion--the percentage of all of Earth's water that is salt water. A parameter could be a standard deviation, a third quartile (Q3), a minimum, a range--anything, as long as it summarizes the population. For instance, the minimum GPA of all students in CT high schools might be a parameter, as it summarizes the population, "all high school students in CT." Although we may not know the value of a parameter, there is some true value; for example, there is an actual, set/fixed age of all humans, or an actual minimum GPA of all hs students in CT, we just don't know what it is

In most cases, we do not know the values of population parameters; it would be nearly impossible to calculate the values above--imagine trying to find the average age of all humans--by the time you found everyone, millions of people would have been born and passed. Some parameters, we do know, like the % of Earth's water that is salt water. Most of the time, we don't know the values of population parameters; one of the most valuable uses for Statistics is to try to estimate these parameters. We try to use sample statistics to estimate parameters; maybe we're trying to estimate the % of all CT residents who will vote for Bernie Sanders, or the median income of all households in Hartford county, or the average amount of rainfall in Florida each year. Even though we don't know these values, they do exist, and they are some fixed value.

Generally, it's too time consuming, cost effective, and sometimes impossible to survey/study an entire population, so we use sample statistics to try to estimate these population parameters. Samples are much more realistic options, and we can use them to accurately predict the values of population parameters.

Sample statistics are values that summarizes samples--any mean, median, standard deviation, IQR, maximum, etc. is a statistic if it is summarizing a sample of data. When we survey 400 students from CT high schools and ask their GPA, then find the mean, minimum, standard deviation, etc. these are statistics because they summarize a sample. We also know that if we take many samples, they will not all yield the same statistics; if you and I both took samples of 400 CT students, we would not get the same sample mean or minimum etc. This is sampling variability (or sampling error)--the idea that sample statistics will vary for different samples, However, in our coming chapters, we will see that we can develop an understanding of how much they vary, and can use this to predict the values of parameters.

So, sample statistics are different for different samples. But by understanding how these sample statistics will vary, we can use them to accurately predict the fixed value that is the population parameter.

Take Home Quiz Questions: