Z score
in a normal distribution it tells you how far a number is above or below mean in terms of standard deviations.
negative
A z score must be ____ whenever it is located in the left half of the normal distribution.
point estimate
The sample mean (x?) is the best ____ of the population mean (?).
point estimate
A single number, based on sample data, that represents a plausible value of a population characteristic
sample mean
The ____ is the best point estimate of the population mean (?).
x?
sample mean
?
population mean
Interval estimate
use a range of values as your estimate of an unknown quantity
Interval estimate
an estimate that the parameter is between two boundary values. These boundary values are also found using sample data
o Confidence level
o Statistic
o Margin of error
Interval estimate consists of three parts:
confidence level
probability that these boundary values, calculated from samples, will lie on either side of the parameter being estimated. Describes the uncertainty of a sampling method
confidence level
the percentage of all possible samples for which the confidence intervals will contain the parameter being estimated; selected subjectively by the researcher.
?
population standard deviation
z score separating an area of ?/2 in the right tail of the standard normal distribution
What does z ?/2 stand for
?
the compliment of the confidence level
1. The population is normally distributed
2. N is at least 30 (n > 30)
Requirements for Confidence Interval for Estimating a Population Mean (with ? known)
a. Confidence level
b. Interval of values
c. Parameter in context
d. Units of measure
Four parts of the concluding statement for a confidence interval
t-distribution
A family of probability distributions that can be used to develop an interval estimate of a population mean whenever the population standard deviation ? is unknown and is estimated by the sample deviation s.
Samples must be taken from a normal population. In other words, the population must be normally distributed.
Requirement when using t-distribution
Z
If you have the mean (?) and population standard deviation (?), which distribution do you use?
t
If you have the mean (?) and sample standard deviation (s), which distribution do you use?
Hypothesis
claim or statement about the value of a parameter
Hypothesis test
a method for determining which hypothesis is correct. This is done by initially assuming that one hypothesis is correct, and using sample data to determine whether that is true.
Null hypothesis
hypothesis initially assumed to be true. We say that it is the hypothesis being tested.
Null hypothesis
Ho
Alternate hypothesis
hypothesis considered to be an alternative to the null hypothesis. The null hypothesis will be rejected in favor of the alternate hypothesis ONLY if the sample data strongly indicate that Ho is false.
always
The symbol for the Null Hypothesis will ___ have an "equal to" part
never
the symbol for the Alternate Hypothesis will ___ have an "equal to" part
Type I error
rejecting the null hypothesis when it is true (i.e., when we shouldn't be rejecting it).
type I error
Denoted ? (alpha)
significance level
The boundary used by the researcher to denote the point at which the null hypothesis will be rejected; also labeled as the alpha level
type I error
Error of rejecting null hypothesis when in fact it is true (also called a "false positive"). You think you found a cause effect relationship but ONE IS NOT THERE
Type II error
not rejecting the null hypothesis when it is false (i.e., when we should be rejecting it)
Type II error
error of failing to reject a null hypothesis when in fact it is false (also called a "false negative"). You think there is NO CAUSE EFFECT but THERE IS
Type II error
denoted ? (beta)
p-value
expresses the degree of belief in the null hypothesis.
p-value
A probability value that shows the statistical level at which chance is likely to have operated on the results obtained from research
less than or equal to
If the P-Value is ___ the level of significance ?, then the decision must be to reject H0.
greater than
If the P-Value is ____ the level of significance ?, then the decision must be to fail to reject H0
lower
The ___ the P-value, the more likely it will be that we will reject the H0.
reject
In other words, if P < ____ Ho.
The sample means must be normally distributed. Verified bc n > (or equal to) 30
What is the requirement sentence you should write for a confidence interval estimate? (for mu with z)