STATS (T DISTRIBUTION AND Z-SCORE)

t-distribution

it is also known as the student's distribution, is used when making inferences about the mean of a small sample when the standard deviation of the population is not known.

bell-shaped

this describes the shape of a distribution in a t-distribution.

degree of freedom

this refers to the number of independent observations in the set of data, or the number of variables that are free to vary.

30

fill in the blank.

the formula for t-distribution is used when the sample size is less than _____.

t = ( x ̅ - μ ) / ( s /√n )

it is the formula for computing the t-score.

t

in the formula, this refers to the student's t-distribution.

x

in the formula, this refers to the sample mean.

μ

in the formula, this refers to the population mean.

s

in the formula, this refers to the sample standard deviation.

n

in the formula, this refers to the sample size.

df = n - 1

it is the formula for the degree of freedom (df).

zero

fill in the blank.

the mean, median and the mode of the t-distribution are all equal to _____.

1 or 100%

fill in the blank.

the total area under the t-distribution curve is ____ or ____.

true

true or false.

the variance is always greater than 1 and is equal to df / df-2.

true

true or false.

the mean, median, and mode coincide at the center.

unknown, 30

fill in the blanks.

the t-distribution is used when the population standard deviation is __________________ and the sample size is less than ______.

z = ( x ̅ - μ ) / ( σ / √n )

this is the formula used if the population variance or standard deviation is known, and if the sample size is 30 or more.

z-score/standard score

it tells how many standard deviation a value is away from the mean.

z = ( X - μ ) / σ

it is the formula for z-score.

x = μ + zσ

in finding the z-score, this is the formula used to find x.

μ = x - zσ

in finding the z-score, this is the formula used to find the mean.

σ = ( X - μ ) / z

in finding the z-score, this is the formula used to find the standard deviation.