probability
Assume regular 52-card deck. What is the probability that three cards are drawn without replacement, and the third card is the first black card?
(26/52)(25/51)(26/50) = .1275
What are the types of experimental design?
Completely randomized, Blocking, and Matched Pairs
A filling machine puts an average of 4 oz of coffee in jars, with a standard deviation of .25 oz. Forty jars filled by this machine are randomly selected. What is the probability that the mean amount per jar filled in the sampled jars is less than 3.9 oz?
A) .0057, B) .0225, C) .0250, D) .0500, E) .3446
A) .0057
What is the Empirical Rule?
Approximates the percentage of values falling within 1/2/3 standard deviations of the mean of a normal distribution (68-95-99.7 rule)
Name all 7 inference tests
1-prop z-test, 2-prop z-test, t-test(1-sample), 2-sample t-test, chi-square GOF test, chi-square test, linear test for slope (linear regression)
Which of the following is an outcome of a binomial experiment?
A) Getting both spades on the first two draws from a standard deck of cards, when the first card is not replaced before the second card is drawn
B) Getting three spades and four hearts out of the first seven draws from a standard deck of cards, when each card is replaced before the next card is drawn
C) Getting three spades out of the first seven draws from a standard deck of cards, when each card drawn is replaced before the next card is drawn
C) Getting three spades out of the first seven draws from a standard deck of cards, when each card drawn is replaced before the next card is drawn
When should experiments be double blind?
When the evaluation is subjective
When is it better to use a relative frequency table than a frequency table?
When the marginal total is significantly unequal
List resistant/non-resistant measures of statistics. (at least three resistant and two non-resistant)
Resistant: Median, Mode, IQR
Non-resistant: Mean, Standard Deviation
What is the difference between the Law of Large Numbers and the Central Limit Theorem?
The Law of Large Numbers focuses on the center, while the Central Limit Theorem discusses the shape of the distribution.
LoLN: the more you sample, the more accurate the mean average becomes
CLT: as n increases, the shape of the distribution becomes more normal
Four MCQ --> probability of missing 0 = .15, missing 1 = .4, missing 2 = .3, missing 3 = .1, missing 4 = .05.
What is the standard deviation of random variable X, the number of problems missed?
Expected value = 1.5
SD = sqrt((0-1.5)^2(.15)+(1-1.5)^2(.4)+(2-1.5)^2(.3)+(3-1.5)^2(.1)+(4-1.5)^2(.05)) = 1.025
What is the difference between response bias and voluntary bias?
Response bias - those who respond to a survey are likely to lie in their answer (typically due to question wording or fear of repercussions from surveyors), resulting in data unrepresentative of a population's true parameter
Voluntary bias - those who choose to respond to a survey are more likely to give a certain answer, resulting in data representative of only those who felt strongly about their answer (extreme data points are overrepresented)
What affects power? (name all four)
1. The significance level of a test
2. The sample size
3. Variability of the response
4. The difference between the hypothesized value and its true value
Using the standard deviation method of finding outliers, are there any outliers in this data set? If so, what are they?
x̄: 38
s: 4.3
Min: 30
Q1: 36.5
Med: 38.5
Q3: 47
Max: 52
Yes, any values in the data set above 50.9 will be outliers
38 + 3(4.3) = 50.9
38 - 3(4.3) = 25.1 (less than min of data set)
Mr. Snider believes that giving his students a practice quiz every week will motivate them to study harder, leading to a greater overall understanding of the course material. He tried this technique for a year, and everyone in the class achieved a grade of at least a C. Is this an experiment or an observational study?
Observational Study
The recommended fitness level with regard to the number of push-ups for an adult male is 34. In a fitness test, a t-test of Ho: u = 34 against Ha: u < 34 gives a p-value of .0068. Using this data, what is the largest level of confidence for a two-sided confidence interval that does NOT contain 34?
85%, 90%, 92%, 95%, or 96%
85%
1 - 2(0.068) = 0.864; anything greater than 0.864 will contain 34
Mr. Bear wants to test the effects of 4 different temperature levels, 2 different types of pans, and 3 different types of ovens on the texture of the cakes, in all combinations. What type of design is this experiment, and how many treatment groups are there?
A completely randomized design with 24 treatment groups
Average body temp. of rat = 37.7°C with 1.2°C SD
Average body temp. of mouse = 36.6°C with 1.8°C SD
With a random sample of 20 rats and 25 mice, is there sufficient evidence at α = .05 to suggest that the rodents' average body temperatures are different?
REJECT Ho at α = .05; with a p-value of .0186 < .05, we have sufficient evidence to conclude that rats and mice have different average body temperatures.
A sampling distribution of how many chocolate chip cookies Snoopy eats a week has a mean of 13 and a standard deviation of 2, there are two outliers in the distribution. Which variable of CUSS is missing?
Which of the following statements about any two events A and B is true?
(A) P(AUB)=0 implies events A and B are independent.
(B) P(AUB)=1 implies events A and B are mutually exclusive.
(C) P(AnB)=0 implies events A and B are independent.
(D) P(AnB)=0 implies events A and B are mutually exclusive.
(E) P(AnB)=P(A)-P(B) implies A and B are equally likely events.
(D) If the probability of the intersection of two events is zero, then those two events cannot both occur. They are disjoint.
Suppose we have a random variable X where the probability associated with the value k is
(15 C k)(.29)^k(.71)^(15-k) fo k=0,...,15.
What is the mean of X?
4.35. This is a binomial with n=15 and p=.29, and so the mean is np=15(.29)=4.35.
Charlie Brown is successful in selling baseball bats to 20 percent of the friends he contacts. He decides to construct a simulation to estimate the mean number of friends he needs to contact before being able to sell a baseball bat. How should he design this simulation using random digits?
Assign numbers 0, 1 to successfully selling a baseball bat and numbers 2-9 as failing to sell a baseball bat. No unusable digits.
Given an experiment with Ho: u=10, Ha: u>10, and a possible correct value of 11, which of the following increases as n increases?
I. The probability of a Type I error.
II. The probability of a Type II error.
III. The power of the test.
III only. As n increases the probabilities of Type I and Type II errors both decrease.
The appraised values of houses in a city have a mean of $125,000 with a standard deviation of $23,000. Because of a new teachers' contract, the school district needs an extra 10% in funds compared to the previous year. To raise this additional money, the city instructs the assessment office to raise all appraised house values by $5,000. What will be the new standard deviation of the appraised values of houses in the city?
$23,000. Adding the same constant to all values in a set will increase the mean by that constant, but will leave the standard deviation unchanged.
Suppose the correlation between two variables is r=.19. What is the new correlation if .23 is added to all values of the x-variable, every variable of the y-variable is doubled, and the two variables are interchanged.
A) .19, B) .42, C) .84, D) -.19, E) -.84
A) .19
The correlation coefficient is not changed by adding the same number to every value of one of the variables, by multiplying every value of one of the variables by the same positive number, or by interchanging the x- and y-variables.