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Binomial Distributions
Inference for Proportions
Exploring Data
General Probability
Sample Designs/Experiements
100
You toss a coin 10 times. What is the probability that you get a heads on the 7th toss?
binomial distribution - success/failure, independent trials, probability of success in constant, n fixed trials p(heads on 7th toss)= 10C7 (.5)^7 (1-.5)^3 calculator : binompdf(10,.5,7) answer: .117
100
What is the test statistic for proportions?
Z*
100
You separate people in your class based on their hair color. What type of data is this?
categorical- hair color is the category.
100
The probability of winning a trip to see Fall Out Boy is .0023. What is the complement of this probability?
Complement= 1 - p(winning the trip) = 1-.0023= .9977
100
A coach compares the swimmer's timings before the new training program and then after the training program. What kind of design is this?
Matched pairs - comparing not using the training program and then using it on one experimental unit (the swimmers).
200
You pick a card 10 times without replacing the card. You want to find the probability of picking an ace of hearts the 4th time. Could you use binomial distribution?
No because in a binomial distribution, the probability needs to be the same throughout. If you don't replace the card, the probability changes after ever trial.
200
The margin of error for a single sample for proportions is z* x mean of sample. Is this correct? If false, correct it.
False- MOE is Z* x (sqrt of [(p hat x 1- p hat)/n])
200
John uses the min, max, Q1, Q3, and mean to create a box plot. Is this right?
No because box plots use the median, not the mean.
200
You cannot pick out an Ace and a King at the same time. These two events are ___________?
Mutually exclusive because they cannot happen at the same time.
200
A person wants to measure the amount of hours students at Charter study. What could be done to make this a stratified random sample?
Use strata. Ex: break the sample into grades: freshman, sophomore, junior, senior
300
The probability of serving a fault in tennis is .3. What is the probability that Sally will hit a good serve in 4 tries? She only has 6 tries.
binomial distribution - yes fault - bad serve p(not serving a fault) = 1-.3 = .7 6C4 (.7)^4 (.3)^2 binompdf (6,.7, 4) = .324
300
You're trying to see if the sample proportion of people with JanSport backpacks is the same as the population proportion. You get a p value of .0009. What is your conclusion?
Since the p- value is small, we reject the null hypothesis. There is significant evidence to suggest that the sample proportion of people with JanSport backpacks is equal to the population proportion.
300
A distribution is skewed to the right. Is it okay to assume that the median is larger than the mean?
No because a median is only larger than the mean if the distribution is skewed right. In this case, the mean would be larger.
300
What is the probability of getting a parrot and a dog if the probability is .2 and .6 respectively?
.12. p(A and B)= p(A) x p(B)= .2 x .6= .12
300
Paulina works at a radio station and wants to know how many people in Texas like Korean pop music. She takes calls and asks people. What could be a problem with this method?
She could have response bias. Some people might jokingly choose an answer or the sample might not be representative of the population as only the people who listen to that particular station would call in.
400
Find the probability that Eugene, who didn't study, would pass a test. He needs to get 8 or more out of the 10 questions to pass.
p(x greater than or equal to 8) = 1- p(x<8) binomcdf(10,.5,7)= .945 1-.945= .05 or p(x=8) + p(x=9) + p(x=10) 10C8 (.5)^8 (.5)^2 +.....+ 10C10 (.5)^10 (.5)^0
400
A Harry Potter fan wants to know the proportion of fans that say Hermione is their favorite. For a 95% confidence interval, he wants his margin of error to be within .05 of the population proportion. How large should the sample be?
sqrt of (.5)(.5)/n times 1.645 = .05 divide both sides by 1.645 . square both sides to get : .25/n = .03^2 n = 277.7 so at least 278.
400
The standard deviation of a set of data is 2.6. If you take away the outlier, would the standard deviation change and if so, how?
Yes, it would decrease. Standard deviation is the measure of how far the data is away from the mean so if there isn't an outlier, the data is that much closer to the mean.
400
What is the probability of choosing the letter e or k on the first try from the word "Kettle?"
disjoint events: p(A or B) = p(A)+ p(B) p(choosing e)= 2/6 p(choosing k)= 1/6 2/6+1/6= 3/6 or 1/2 probability of choosing an e or a k on the first try.
400
Trenton wants to see how many people help an old lady cross the street. He presents his experiment to his class. What is wrong with that last sentence?
Trenton did an observational study because he had no independent variable. He just observed what happened and recorded it. This is not an experiment.
500
Mac wants a milkshake. There are 10 different kinds of milkshakes on the menu and Mac likes 4 of out these 10. Mac has to randomly choose a milkshake. What is the probability that it will take 3 or fewer tries to pick a milkshake he likes?
p(x less than or equal to 3)= p(x=0) + ....+ p(x=3) 10C0 (.4)^0 (.6) ^10 + ..... 10C3 (.4)^3 (.6)^7 or binomcdf(10,.4,3)= .382
500
The sample proportion of people in Class 1 who like Pepsi is 18/33. The sample proportion of people in Class 2 who like Pepsi is 16/22. To test for proportion, would it be ok to use the population proportion (.6)? If not, what should you use and what would be the value.
No, you need to use p hat which is (X1+X2)/(n1+n2) the value of p hat would be: .62
500
Some data's 5 number summary is : min - 35 Q1- 50 Q3-70 median- 63 max-85 What is the interquartile range and what numbers would be considered outliers?
IQR= Q3-Q1= 70-20=50 below: Q1- 1.5(50)=-25 above: Q3+ 1.5(50)=145
500
A jar has red and green skittles. You randomly pick 2 skittles without replacing the first one. p(getting a red and then a green)= .28. The p(getting a red on the first try)= .37. What is the probability of picking a green skittle on the second try, provided that you pick a red skittle first?
.756 p(BlA)= p(A and B)/ p(A) p(greenlred) = .28/.37= .756
500
Rose wants to test a type of soil for her plants. She uses the new soil on the half that receives a lot of sun but not the other side. What is the problem with this?
The variables are confounded- You can't tell if the plants grew because of the sun or the type of soil.