Download Chapter 7 Terms and Formulas

Chapter 7
Central limit theorem
The central limit theorem says that x can have any distribution whatsoever, but as the sample
size gets larger and larger, the distribution of x bar will approach a normal distribution.
(For more information, review Section 7.5)
Continuity correction
Adjusting the values of discrete random variables to obtain a corresponding range for a
continuous random variable is called making a continuity correction. If the discrete variable is a
left point of an interval, subtract 0.5 to obtain the corresponding normal variable. If the discrete
variable is a right point of an interval, add 0.5 to obtain the corresponding normal variable.
(For more information, review Section 7.6)
Empirical rule
For a distribution that is symmetrical and bell-shaped (in particular, for a normal distribution):
Approximately 68% of the data values will lie within one standard deviation on each side of the
mean. Approximately 95% of the data values will lie within two standard deviations on each side
of the mean. Approximately 99.7% (or almost all) of the data values will lie within three
standard deviations on each side of the mean.
(For more information, review Section 7.1)
z value or z score
The z value or z score gives the number of standard deviations between the original
measurement x and the mean of the x distribution.
(For more information, review Section 7.2)
Left-tail style table
A left-tail style table gives cumulative areas to the left of a specified z.
(For more information, review Section 7.2)
Normal curve
The graph of a normal distribution is called a normal curve.
(For more information, review Section 7.1)
Normal distribution
One of the most important examples of a continuous probability distribution is the normal
distribution.
(For more information, review Section 7.1)
Normal quantile plot
A normal quantile plot is an indicator that can be used to determine if data have a normal
distribution. For data that approximately havea a normal distribution, the normal quantile plot of
the data should have points close to a straight line.
(For more information, review Section 7.3)
Pearson's index
Pearson's index is a measure of skewness for sample data. Normal distributions are symmetric
and should have a Pearson's index value between –1 and 1.
(For more information, review Section 7.3)
Raw score
The raw score is the value of a random variable in a non-standard normal distribution. The raw
score can be converted into a z score.
(For more information, review Section 7.2)
Sampling distribution
A sampling distribution is a probability distribution of a sample statistic based on all possible
simple random samples of the same size from the same population.
(For more information, review Section 7.4)
Standard error
The standard error is another name for the standard deviation of the x bar distribution.
(For more information, review Section 7.5)
Standard normal distribution
The standard normal distribution is a normal distribution with mean 0 and standard deviation 1.
(For more information, review Section 7.2)
Unbiased
A sample statistic is unbiased if the mean of its sampling distribution equals the value of the
parameter being estimated.
(For more information, review Section 7.5)