CH 16: LAW OF AVERAGES
A box contains 10,000 tickets: 4,000 0 6,000 1. 10,000 draws are made at random with replacement from this box. The number of 1s will be ______________. (Don't calculate the EV, just speak in terms of law of averages)
The number of 1s is likely to be different from 6,000, but the difference is likely to be small compared to 10,000!
What is the average and SD of the box
1 1 3 3 5
Average = 2.6
SD = 1.497
The probability histogram for the sum of the draws will be close to the normal curve even if the tickets in the box do not follow the normal curve, as long as the number of draws is large enough.
True!
Identify the sample, population, statistic, and parameter:
A public health administrator wants to estimate the average age of Utah residents who have had Covid-19. To do this, she takes a simple random sample of 1000 Utah residents from all of those who have tested positive for Covid-19 and finds out their ages
Population: UT residents that had COVID
Sample: Selected 1000 UT residents that had COVID
Parameter: Avg age of all UT residents that had COVID
Statistic: Avg age of of the selected 1000
How many decimal points should you round values to until you've arrived at a final answer?
3 or more!!
A gambler loses ten times running at roulette. He decides to continue playing because he is due for a win, by the law of averages. A bystander advises him to quit, on the grounds that his luck is cold. Who is right?
They both are wrong! His odds of winning are the same every time.
400 draws will be made with replacement from the box:
2 4 6 8
You expect the sum of the draws to be ______ give or take ______
Expect the sum of the draws to be 2000 give or take 44.72
If we look at the sum of 10 draws from a box, the probability histogram for the sum of the draws will follow the normal curve even if the histogram for the tickets in the box is far from the normal curve.
False! 10 is not enough draws!
What are the pros and cons to Simple Random Sampling?
Pro: best way to get a sample that is representative of the population
Con: can be expensive and difficult to put into practice
Where in FWS should you go if you want to know the chance of observing a sum of BLANK or more
Shade under (standard) normal curve
A die will be rolled some number of time, and you win $1 if it shows an ace more than 20% of the time. Which is better: 60 rolls, or 600 rolls? EXPLAIN!
60 rolls! We want the short run, because we know that in the long run we will see an ace about 16% of the time.
A gambler will play roulette 50 times, betting a dollar on four joining numbers each time. This bet pays 8 to 1, and there are 4 chances in 38 of winning.
Set up the box model for the winnings!
| 4 8 34 -1 | ---> 50
Fifty draws are made at random from the box
2 2 3 3 4
Describe the probability histogram for the sum of the draws
Approximately normal (centered at the EVsum and SEsum)
To survey the opinions of USU students, an administrator takes a simple random sample of 10 majors. He gives the survey to all students who have declared one of these majors.
Which sampling method is being utilized here?
Cluster sampling
When you are modeling the probability histogram of the sum in FWS, what should you enter in as the average and SD of the curve?
EVsum for Average and SEsum for SD!!
Two hundred draws will be made at random with replacement from the box -3 -2 -1 0 1 2 3. In general, how can you figure out the average of the 200 draws, if you are told their sum?
average = sum/200
In a game of chance, a player rolls a 6-sided die. If the die lands on a 1 or a 2, the player loses $3, if it lands on a 3 or 4 they lose $6, if it lands on a 5 they win $3, and if it lands on a 6 they win $15. If we play the game 50 times, the player expects to win $_____ give or take $_____
Expect to win $0.00 give or take $51.97
A pair of dice are thrown. The total number of spots is like one draw from the box: 2 3 4 5 6 7 8 9 10 11 12 or like two draws from the box: 1 2 3 4 5 6
Two draws from the box: 1 2 3 4 5 6
To survey the opinions of USU students, an administrator takes a simple random sample of 10 majors. He gives the survey to all students who have declared one of these majors.
T or F: This sample has non-response bias
False!! This shows selection bias, not nonresponse.
Share 3 test-taking strategies you've found helpful in this class :)
Some of Madi's favs:
Read the question carefully. After you think you have an answer, read the question again and make sure what you've done has answered that question!
Take your first attempt as early as you can so that you have time before your second attempt to put in some extra studying!
If you're not sure how to do a question, flag it and move on. When you're ready to come back to it, take a deep breath and fresh eyes will help!
Two hundred draws will be made at random with replacement from the box -3 -2 -1 0 1 2 3. I want as high of a sum as possible. What's better a sum of 210 or an average of 1.05?
They're the same!
In a game of chance, when the coin flips heads I get $3 and when it flips tails I lose $4. What is the chance that I at least break even in 400 coin flips?
0.21%
I make 50 draws from the following box:
| 99 1 1 0 |
True or False: The probability histogram of the sum of the draws will be approximately normal
False! Because the box is SO skewed we will need a larger number of draws.
A survey wants to know what proportion of women find red hair attractive. The person running the survey has red hair. What type of bias is present in this survey?
Response bias!
What do you need to do if you want your lowest test score to be dropped? (REMINDER: The final is worth 30% of your grade in the course and cannot be dropped)
Take Optional Test 6