Unit 1:
Intro
Intro
A student selects their roommates as the sample to represent the population of their dorm hallway. This is known as _______ sampling.
An R value of ______ indicates a horizontal line--or a completely random spattering--of data points on a scatter plot.
What is 0?
Consider these events to be independent:
1. You roll a six-sided die
2. You flip a coin
What is the probability of rolling a 6 followed by a heads?
P(X = 1) = 0.22
P(X = 2) = 0.10
P(X = 3) = 0.44
P(X = 4) = 0.24
The expected value, E(X), is _____.
What is 2.4?
1*.22 + 2*.10 + 3*.44 + 4*.24 = 2.7
Matt is interested in the heights of students at the University of Iowa. In his sample, he found a sample variance of 9 inches. What is the sample standard deviation?
What is 3?
sqrt(9) = 3
s^2 = sample variance
s = sample standard deviation
You are interested in predicting profit given days of operation of a business. The resulting regression equation is:
Y_hat = 11.809x + 40.363
Predict the profit on the 17th day of operation.
What is $241.11?
y_hat = 11.809*17 + 40.363
P(AC) = ?
What is 1 - P(A)?
A company is launching a new marketing campaign and is tracking the number of calls made by a salesperson until they reach a successful sale. The probability of making a sale on any given call is 0.20. Let X be the number of calls made until the first sale occurs. The variance of X is ____.
What is 20?
Var(X) = (1 - 0.20) / 0.20^2 = 20
Consider the random sampling of Iowa students to determine how often they eat at Mickey's which is recorded as "once or more a week," "once or more a month," "once or more a year," and "never." The kind of variable being used here is a ______ variable.
What is categorical?
A student mistakenly flips their x and y axes when creating a scatterplot. This would ______ the data's correlation coefficient.
The probability that George gets an A in a class is 0.5, whereas the probability his friend gets an A in that class is 0.6. The probability they both get an A is 0.3. The probability that only George gets an A is ____.
What is 0.2?
A company sells a product, and the probability that a customer buys it is 0.3. Let X1 be the number of customers a company has to approach until the first one buys the product. Let X2 be the number of customers who buy the product in a group of 10 customers.
P(X1 = 4) = _____
What is 0.1029?
P(X1 = 4) = (1 - 0.3)3 * 0.3 = 0.1029
The average time spent studying per week by all University of Iowa students is 6 hours. You conduct a simple random sample of University of Iowa students and discover the sample's average weekly studying time to be 4.8 hours with a standard deviation of 0.5 hours.
Calculate (x_bar - mu) / s2
What is -4.8?
(4.8 - 6) / 0.52 = -4.8
You are interested in predicting profit given days of operation of a business. The resulting regression equation is:
Y_hat = 11.809x + 40.363
Given that the business actually earned 112 dollars on their 6th day of operation, calculate the residual for X = 6.What is $0.79?
= $112 - $111.2154 = $0.785
What is .1324?
P(A intersect B) = 0.21 + 0.68 - 0.80 = 0.09
P(A|B) = 0.09 / 0.68 = .1324
In a survey, 5 people are randomly chosen, and, for each person, there is a 70% chance they support a certain candidate. Let X be the number of people who support the candidate out of the 5. The probability that exactly 3 people support the candidate is ______.
What is 0.3087?
n = 5 | x = 3 | p = 0.7
P(X=3) = (5 choose 3) * (0.7)3 * (0.3)5-3 = 0.3087
A vending machine sells four types of sodas. At the beginning of the week, a worker stocks 75 of each type of soda into the machine. At the end of the week, the worker noticed 35 cans of Soda 1 left, 22 cans of Soda 2 left, 64 cans of Soda 3 left, and 12 cans of Soda 4 left. What is the cumulative frequency of Soda 3 being taken?
Soda 1: 75 - 35 = 40
Soda 2: 75 - 22 = 53 | 40 + 53 = 93
Soda 3: 75 - 64 = 11 | 93 + 11 = 104
The coefficient of determination for your linear regression model is 0.74. If your regression line is positive (i.e., upwards-sloping), what is your model's correlation coefficient?
What is 0.86?
sqrt(0.74) --> works only because r is positive (positive relationship indicated by the upwards-sloping regression line)
A rare disease affects 5% of a population. A new diagnostic test has been developed to detect this disease. However, the test is not perfect. If a person has the disease, the probability the test correctly detects it is 95%. If a person does NOT have the disease, the probability that the test correctly returns negative is 90%.
Suppose a person is randomly selected from the population, and they test positive for the disease. What is the probability this person actually has the disease?
What is 0.33?
P(D) = 0.05 | P(~D) = 0.95
P(T+|D) = 0.95 | P(T+|-D) = 1 - .90 = 0.10
P(T+) = P(T+|D)*P(D) + P(T+|-D)*P(-D) Total Probability
P(T+) = 0.95*0.05 + 0.10*0.95 = 0.1425
P(D|T+) = P(T+|D)*P(D) / P(T+)
P(D|T+) = (0.95)*(0.05) / 0.1425 = 0.3333
Imagine you are the line manager at a very large factory. Assume each product is either defective or not defective. The non-defective rate for each product is 88%. The probability the first defective product is found between the 5th and 9th product (inclusive) is ____.
What is 0.2832?
p = 1 - .88 = .12P(X<=9) = 1 - (1-.12)|9| = 0.6835
P(X<=4) = 1 - (1-.12)|4| = 0.4003
P(5<=X<=9) = 0.6835 - 0.4003 = 0.2832