Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
31 Cards in this Set
- Front
- Back
|
standard normal distribution has these three properties:
|
1) its graph is bell shaped
2) its mean is equal to 0. ( µ = 0) 3) its standard deviation is equal to 1. |
|
|
A continuous random variable has a uniform distribution if:
|
its values are spread evenly over the range of possibilities.
|
|
|
The standard normal distribution is:
|
a normal probability distribution with µ = 0 and σ = 1.
|
|
|
The total area under the density curve of a standard normal distribution is equal to:
|
1
|
|
|
The graph of a continuous probability distribution is called a:
|
density curve
|
|
|
Because the total area under the density curve is equal to 1, there is a correspondence between:
|
area and probability
|
|
|
What is the procedure for finding the AREA of a normal distribution between two z-scores on the TI-84?
|
Press 2nd, Distr, normal cdf(z-score, z-score), enter
|
|
|
With any continuous random variable, the probability of any one exact value is:
|
zero
|
|
|
What is the procedure for finding a Z-SCORE from a known area on the TI-84?
|
press 2nd, distr, invNorm, enter area to the left of the z-score.
|
|
|
Is it possible to convert a non-standard normal distribution to a standard normal distribution?
|
yes
|
|
|
What is the procedure for converting a non-standard normal distribution to a standard normal distribution?
|
1) sketch a normal curve, label the mean and x values, and shade the desired region.
2) convert the desired x value into an equivalent z-score using the z-score formula: z = x - µ / σ 3) Use the z-score to find the area |
|
|
What is the procedure for finding values from known areas of a non-standard normal distribution?
|
1) sketch a normal curve, label the percentage or area, and identify the x values being sought.
2) Use table A-2 to find the z-score corresponding to the cumulative left area bounded by x. The area given will be in the BODY of the table. The values at the margins are the z-scores. 3) Use the z-score formula to find the value of x. |
|
|
Which statistics are unbiased estimators, and which are biased estimators?
|
Mean x̅, Variance s², and Proportion P̂ are unbiased.
Median, Range, and Standard deviation are biased. |
|
|
The distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.
|
The sampling distribution of a statistic
|
|
|
The distribution of sample means, with all samples having the same sample size n taken from the same population.
|
The sampling distribution of the mean
|
|
|
The distribution of sample variances, with all samples having the same sample size n taken from the same population.
|
The sampling distribution of the variance.
|
|
|
The distribution of sample proportions, with all samples having the same sample size n taken from the same population.
|
The sampling distribution of the proportion.
|
|
|
Notation for proportions:
p = p̂ = |
p = population proportion
p̂ = sample proportion |
|
|
The central limit theorem tells us that:
|
for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.
|
|
|
In the central limit theorem:
-The mean of the sample means = -The STDV of the sample means = |
= population mean (µ)
= σ /√(n) where n is the sample size |
|
|
When selecting a simple random sample of n subjects from a pop. with mean µ and STDV σ, it is essential to know these principles:
|
1) For a pop. with any distr., if n > 30, then the sample means have a distr. that can be approximated by a normal distr. with mean µ & STDV of σ /√(n).
2) If n ≤ 30, and the orig. pop. has a normal distr., then the sample means have normal distr. with mean µ and STDV of σ /√(n). 3) If n ≤ 30 and the orig. pop. doesn’t have a normal distr., then Central limit theorem doesn’t apply. |
|
|
the mean of the sample means is denoted by:
|
µᵪ̅
thus, µᵪ̅ = µ |
|
|
the STDV of the sample means is denoted by:
|
σᵪ̅
thus, σᵪ̅ = σ /√(n) |
|
|
σᵪ̅ is called:
|
the standard error of the mean.
|
|
|
When can we automatically use the central limit theorem?
|
If the sample size is greater than 30 or, if the original population is normally distributed.
|
|
|
When do you use the central limit theorem and when do you not?
|
-Use the central limit theorem when working with a mean of some sample.
-Use the normal distribution methods when working with an individual value. |
|
|
What is the z formula when working with an individual value?
What is the z formula when working with the mean of some sample? |
individual value: z = x - µ / σ
sample means: z = x̅ - µ / [σ /√(n)] |
|
|
What is the rule of thumb when correcting for a finite population?
|
When sampling without replacement and the sample size n is greater than 5% of the finite population size N, adjust the standard deviation of the sample means σᵪ̅ by multiplying it by the finite population correction factor.
|
|
|
The finite population correction factor is:
|
√[(N - n) / (N - 1)]
|
|
|
What is the requirement for approximating a binomial distribution?
|
np ≥ 5 and nq ≥ 5
|
|
|
What are the procedures for approximating a binomial distribution?
|
1) Check: np ≥ 5 and nq ≥ 5
2) Find µ and σ. 3) Identify x. 4) Draw continuity correction 5) Examine: at least, more than, etc. 6) Find z-score using x value from step 5. |
