Stats 5 Ch. 06

Front 1

standard normal distribution has these three properties:

Back 1

1) its graph is bell shaped
2) its mean is equal to 0. ( µ = 0)
3) its standard deviation is equal to 1.

Front 2

A continuous random variable has a uniform distribution if:

Back 2

its values are spread evenly over the range of possibilities.

Front 3

The standard normal distribution is:

Back 3

a normal probability distribution with µ = 0 and σ = 1.

Front 4

The total area under the density curve of a standard normal distribution is equal to:

Back 4

1

Front 5

The graph of a continuous probability distribution is called a:

Back 5

density curve

Front 6

Because the total area under the density curve is equal to 1, there is a correspondence between:

Back 6

area and probability

Front 7

What is the procedure for finding the AREA of a normal distribution between two z-scores on the TI-84?

Back 7

Press 2nd, Distr, normal cdf(z-score, z-score), enter

Front 8

With any continuous random variable, the probability of any one exact value is:

Back 8

zero

Front 9

What is the procedure for finding a Z-SCORE from a known area on the TI-84?

Back 9

press 2nd, distr, invNorm, enter area to the left of the z-score.

Front 10

Is it possible to convert a non-standard normal distribution to a standard normal distribution?

Back 10

yes

Front 11

What is the procedure for converting a non-standard normal distribution to a standard normal distribution?

Back 11

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

Front 12

What is the procedure for finding values from known areas of a non-standard normal distribution?

Back 12

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.

Front 13

Which statistics are unbiased estimators, and which are biased estimators?

Back 13

Mean x̅, Variance s², and Proportion P̂ are unbiased.
Median, Range, and Standard deviation are biased.

Front 14

The distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.

Back 14

The sampling distribution of a statistic

Front 15

The distribution of sample means, with all samples having the same sample size n taken from the same population.

Back 15

The sampling distribution of the mean

Front 16

The distribution of sample variances, with all samples having the same sample size n taken from the same population.

Back 16

The sampling distribution of the variance.

Front 17

The distribution of sample proportions, with all samples having the same sample size n taken from the same population.

Back 17

The sampling distribution of the proportion.

Front 18

Notation for proportions:
p =
p̂ =

Back 18

p = population proportion
p̂ = sample proportion

Front 19

The central limit theorem tells us that:

Back 19

for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.

Front 20

In the central limit theorem:
-The mean of the sample means =
-The STDV of the sample means =

Back 20

= population mean (µ)
= σ /√(n) where n is the sample size

Front 21

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:

Back 21

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.

Front 22

the mean of the sample means is denoted by:

Back 22

µᵪ̅
thus, µᵪ̅ = µ

Front 23

the STDV of the sample means is denoted by:

Back 23

σᵪ̅
thus, σᵪ̅ = σ /√(n)

Front 24

σᵪ̅ is called:

Back 24

the standard error of the mean.

Front 25

When can we automatically use the central limit theorem?

Back 25

If the sample size is greater than 30 or, if the original population is normally distributed.

Front 26

When do you use the central limit theorem and when do you not?

Back 26

-Use the central limit theorem when working with a mean of some sample.
-Use the normal distribution methods when working with an individual value.

Front 27

What is the z formula when working with an individual value?
What is the z formula when working with the mean of some sample?

Back 27

individual value: z = x - µ / σ
sample means: z = x̅ - µ / [σ /√(n)]

Front 28

What is the rule of thumb when correcting for a finite population?

Back 28

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.

Front 29

The finite population correction factor is:

Back 29

√[(N - n) / (N - 1)]

Front 30

What is the requirement for approximating a binomial distribution?

Back 30

np ≥ 5 and nq ≥ 5

Front 31

What are the procedures for approximating a binomial distribution?

Back 31

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.