Tonight, please complete the 2 AP problems provided in class (or below). Here are some hints:
- For part a of the 2010 FR, when asked to "describe the sampling distribution," you must....
- First, check conditions (like #23 from last night's hw)
- Then, define the shape, center, and standard deviation of the sampling distribution
- For question b of the 2010 FR, you need to calculate a probability using the sampling distribution--take a look at today's notes about rainfall in Ithaca, NY!
- Remember, a sampling distribution is about the mean of a sample...
- So, if we have 160 minutes for 4 songs, to exceed the time limit the average length of a song would have to be longer than 4 minutes! (160 min/40 songs = 4 min per song, on ave)
- Check out the AP Scoring Rubric! (2010)
- On the back, you can approach this problem in two ways..
- You can skip the conditions for the problem on the back about the elevator, b/c this was a multiple choice question on the AP exam (skip conditions for MC!).
- First, you could use a sampling distribution for means--think about what the mean of the sample (of 3 men) would have to be over if their total weight exceeds 700 lbs! (In other words, what would the average weight for one male exceed if the 3 men combined are over 700 lbs?)
- Then, use the sampling distribution/Normal model math like our Ithaca example!
- OR....\
- You could approach this problem as we did in chapter 17...
- You could use the individual weights to find the mean and standard deviation if we combine three weights (remember, we can't add standard deviations...Pythagorean Theorem of Statistics...)
- Then, we can use this new mean and standard deviation (and the Normal model) to find the probability that the total weight exceeds 700 lbs!
Tomorrow we will wrap up our notes on Sampling Distributions. You will have a multiple choice take home quiz for homework, and our chapter 18 vocab quiz will be on Monday! Here's the list:
- 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...
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