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Statistics 1 - Chapter 06
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Terms in this set (27)
Normal Distribution
Bell-shaped curve that results when the values of a trait in a population are plotted against their frequency.
Uniform Distribution
A rare type of population distribution where the population is evenly spread out. Results in a rectangular shape.
Standard Normal Distribution
Normal distribution with a mean of 0 and a standard deviation of 1.
z score
A measure of how many standard deviations you are away from the norm (average or mean).
Area
Region under the curve.
Z Score Notation
P(a < z < b) = denotes the probability that the z score is between a & b.
P(z > a) = denotes the probability that the z score is greater than a.
P(z < b) = denotes the probability that the z score is less than a.
Percentile
When given a percentile, such as P95, they are asking what value separates the top 5% from the bottom 95%.
Critical Value
(Book) In a normal distribution, this is the z score on the borderline separating the z scores likely to occur and those that are unlikely. Typical values are -1.96 & 1.96.
(Auto Definition) The value of a statistic required in order to consider the results significant.
Z score notation
The expression z(sub)α denotes the z score with the area of α to its right.
Z score formula
The value minus the mean, divided by the standard deviation.
(x - μ) / σ
Sampling Distribution of a Statistic
Distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.
You plot this by frequency vs sample value.
Sampling Distribution of the Mean
Distribution of sample means, with all samples having the same sample size n taken from the same population.
You plot this by frequency vs sample means.
Ex: Sampling procedure = roll a die 5 times and find the mean. Population average = 3.5
Sampling Distribution of the Variance
Distribution of sample variances, with all samples having the same sample size n taken from the same population.
You plot this by frequency vs sample variances.
Ex: Sampling procedure = roll a die 5 times and find the variance, s squared. Population variance = 2.9
Sampling Distribution of the Proportion
Distribution of the sample proportions, with all samples having the same sample size n taken from the same population.
You plot this by frequency vs sample proportions.
Ex: Sampling procedure = roll a die 5 times and find the proportion of odd numbers. P = 0.5
Sample Standard Deviation Formula
sum of [ (sample value minus sample average) squared] divided by numbers of samples less one.
Sample Variance Formula
Square root of sample standard deviation
Population Standard Deviation Formula
sum of [ (value minus population average) squared] divided by population number
Population Variance Formula
Square root of population standard deviation
Notation for the Sampling Distribution of x-bar
If all possible random samples of size n are selected from a population with mean μ and standard deviation σ, the mean of the sample means is denoted by μ(sub)x-bar.
Also, the standard deviation of the sample means is denoted by σ(sub)x-bar. This is also called the "Standard Error of the Mean".
Central Limit Theorem
The sampling distribution of the mean will approach the normal distribution as N (sample size) increases.
Applying Central Limit Theorem to Z Score
(Sample mean minus population mean) divided by (population standard deviation divided by the square root of N)
In normal words: Difference between sample mean and population mean divided by the standard error.
Rare Event Rule for Inferential Statistics
If the probability of a particular observed event is exceptionally small, such as under 5%, we conclude that the assumption is probably not correct.
Correction for a Finite Population
When sampling w/o replacement and the sample size n is greater than 5% of the finite population size N, adjust the standard deviation of sample means σ(sub)x-bar by multiplying it by the finite population correction factor.
Distribution of Sample Means
Pop is Normal, Dist is normal, sample mean = pop mean
n>30, Dist is normal, sample mean = pop mean
n<=30, Dist is not normal, sample mean = pop mean
I'm not sure what this is saying.
Continuity Correction
When we use the normal distribution as an approximation to the binomial distribution, a continuity correction is made to a discrete whole number x in the binomial distribution by representing the discrete whole number x by the interval from x - 0.5 to x + 0.5.
Purpose behind "Continuity Correction"
When you use a normal distribution with discrete data and need to find a success % for a specific value..
If your value is 2000 out of 2500 people for whatever measured trait, it's n=2500 & x=2000. p=0.8 & q=0.2.
Just figure out the z score of 2499.5 & 2500.5. Find the success between those two values, and ta-da!
Normal Quantile Plot
Graph of Points (x,y) where each x value is from the original set of sample data, and each y value is the corresponding z score that is a quantile value expected from the standard normal distribution.
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Verified questions
PROBABILITY
A coin having probability .8 of landing on heads is flipped. A observes the result—either heads or tails—and rushes off to tell B. However, with probability .4, A will have forgotten the result by the time he reaches B. If A has forgotten, then, rather than admitting this to B, he is equally likely to tell B that the coin landed on heads or that it landed tails. (If he does remember, then he tells B the correct result.) (a) What is the probability that B is told that the coin landed on heads? (b) What is the probability that B is told the correct result? (c) Given that B is told that the coin landed on heads, what is the probability that it did in fact land on heads?
PROBABILITY
A regular tetrahedron and a sphere have the same surface area. If the radius of the sphere is 10 cm, calculate: a) the area of one face of the tetrahedron, b) the length of each edge of the tetrahedron. (Hint: Use the trigonometric formula for the area of a triangle.)
STATISTICS
A carpenter is using a tape measure to get the length of a board. a) What are some possible sources of bias? b) Which is more subject to bias, a steel tape or a cloth tape? c) Would the bias in a cloth tape change over time?
QUESTION
The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 36 bids from potential buyers to estimate the average Joss in home value. The sample showed the average loss was $9560 with a standard deviation of$1500. What assumptions and conditions must be checked before finding a confidence interval? How would you check them?
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