Chapter 6 Flashcards
Standard normal distribution
- Bell shaped graph
- Mean = 0
- SD = 1
- Area under curve = 1
- Correspondence between area and probability.
Uniform distribution
Values are spread evenly
Continuous density curve
- Area under curve = 1
2. Every point on the curve > 0
Less than z score problems
Use number from chart
More than z score problems
1 - number from chart
In between 2 z score problems
Bigger probability - smaller probability
P(a < z < b)
P that a z score is between a & b
P(z > a)
P z score greater than a
P(z < a)
P z score is less than a
In between 2 probabilities problem
Find z score 1-the positive
Critical value
z score on the boarder of likely to occur vs unlikely
Zα
Z score of α area to the RIGHT
Nonstandard normal distribution formula
z= x-μ/α (round z scores to 2 decimal places)
Nonstandard normal distribution between 2 #s
First find z scores, then subtract probabilities
Distences
Z scores
Areas, regions
Probability
Nonstandard normal distribution: finding z score
Use P to find Z then, x=μ+(z*α)
Sampling distribution of a statistic
The distribution of all values when al possible samples are the same size from the same population. (usually displayed as a probability distribution.
Sampling distribution of a mean
Distribution of means of all samples of the same size of the same population. Mean of means is Pop mean. Normal distribution.
Sampling distribution of a variance
Distribution of all variances of all samples of the same size of the same population. Mean of variances is Pop variance. Skewed to the right.
Sampling distribution of a proportion
Distribution of a specified proportion of all samples of the same size of the same population. Mean of proportion is Pop mean. Normal distribution.
Biased estimators
Do not target (represent) the population parameter when repeated indefinitely on samples. Include median, range, and SD. SD bias is small in large samples.
Population σ^2
Σ(x-μ^2)/N
Sample s^2
nΣ(x^2)-(Σx)^2/n(n-1)
Notation of proportions
p=pop proportion ^p=sample proportion
Expected value of sampling distribution statistic
Mean of the sample statistics, and the expected value of the population
Find Zσ/2
Take 1- given number/2 look on A2 find Z
