Terms and Definitions
This is the distribution of possible values of a statistic from all possible samples of the same size from the same population
What is a Sampling Distribution?
This is the assumption that a sampling distribution will be approximately normal if the sample size is sufficiently large, regardless of the shape of the population that the samples are drawn from.
What is the Central Limit Theorem?
The sampling distribution of a sample proportion is approximately normal when these two conditions are met.
Sample size must be less than 10% of the population when sampling without replacement.(10% condition)
Sample size is large enough that np and n(1-p) are greater than or equal to 10. (Large Count Condition)
mu
What is the mean of a population?
Mrs. McCall taught summer school at Chapel Hill High School, but her first year long teaching job was at this school.
What is Cary High School?
This is a number or measurement that describes a population.
What is a parameter?
State the formula we learned to find the standard deviation of a sample mean.
sigma(xbar) = sigma/sqrt(n)
State the formula we learned to find the standard deviation of a sample proportion.
sigma(p-hat) = sqrt((p(1-p))/n)
p-hat
What is a sample proportion?
What is Coffee?
This is a number or measurement that describes a sample
What is a statistic
In Weaksauce City, the mean length of a stay in hospitals is 5.5 days with standard deviation of 2.6 days. This distribution can't be normal, however, because hospital visits for specific injuries skew the graph strongly to the right. Consider random samples of size 100 taken from the distribution with the mean length of stay, xbar, recorded for each sample. Describe the sampling distribution of xbar.
What is approximately normal, with mean = 5.5 days and standard deviation = 0.26 days
Suppose 0.60 (=60%) of all voters (there are over 50,000) in Oswego County intend to vote for candidate Brown in the upcoming election. A random sample of 100 voters is taken. Find the probability that less than half of the sample intend to vote for candidate Brown.
What is 2.061%
sigma
What is a population standard deviation?
This movie/book trilogy is centered around a single piece of jewelry and a long, painful journey that a group of 9 friends go through to destroy it.
What is Lord of the Rings?
A statistic used to estimate a parameter is said to be this, if the mean of its sampling distribution is equal to the true value of the parameter being estimated.
What is unbiased?
The scores of individual students on the ACT follow a normal distribution with mean = 18.6 and standard deviation = 6.0. A random sample of 36 students from JP2 is found to have an average ACT score of 26. We conclude...
What is "it is extremely unlikely to have a sample mean of 26 from the overall population, so we can conclude that JP2 likely has a higher average ACT score"
A SRS of 50000 Americans found that 61% were satisfied with the service provided by the dealer from which they bought their car. A SRS of 1000 Canadians found that 58% were satisfied. Compare the sampling variability associated with these two statistics.
Mux-bar
This famous hero often performs as Marvel's flagship character and stands as one of their most memorable single heroes in the Marvel universe due to his every-man nature and down-to-earth struggles as a high school student and young man.
Who is Spiderman?
For a reliable statistic, we want these two things.
What are low bias and low variability?
At a candle company, machine 1 produces candles with a mean length of 15 cm and a sd of 0.15 cm. Machine 2 produces candles with a mean lenght of 15 cm and a sd of 0.10 cm. Random samples of 49 are taken from each machine. Describe the sampling distribution of x-bar (M1) minus x-bar (M2).
What is "normal due to CLT and 49>30, center is 0, stanard deviation is 0.026?" 10% condition holds because 49<0.10(all candles made by each machine).
Assume that 2% of all products that come off a company's assembly line are defective. The company produces thousands each day. An SRS of 500 of these products is drawn. What is the probability that more than 3% are defective?
What is 5.511%
sigmap-hat1 - p-hat2
The standard deviation of the sampling distribution for a difference in sample proportions
This team called a timeout in the final seconds of the 1993 NCAA championship basketball game, sealing the victory for their opponent.
Who is the University of Michigan?
(Chris Weber)