Description Usage Arguments Details Value Null Hypothesis Test Assumptions Confidence Interval Author(s) References See Also Examples
This function is based on the standard normal distribution and creates confidence intervals and tests hypotheses for both one and two sample problems.
1 2 
x 
numeric vector; 
y 
numeric vector; 
alternative 
character string, one of 
mu 
a single number representing the value of the mean or difference in means specified by the null hypothesis 
sigma.x 
a single number representing the population standard
deviation for 
sigma.y 
a single number representing the population standard
deviation for 
conf.level 
confidence level for the returned confidence interval, restricted to lie between zero and one 
If y
is NULL
, a onesample
ztest is carried out with x
. If y is not NULL
, a standard
twosample ztest is performed.
A list of class htest
, containing the following components:
statistic 
the zstatistic, with names attribute 
p.value 
the pvalue for the test 
conf.int 
is a confidence interval (vector of length 2) for the
true mean or difference in means. The confidence level is recorded in the attribute 
estimate 
vector of length 1 or 2, giving the sample mean(s) or mean of
differences; these estimate the corresponding population parameters. Component

null.value 
is the value of the mean or difference in means specified by
the null hypothesis. This equals the input argument 
alternative 
records the value of the input argument alternative:

data.name 
a character string (vector of length 1) containing the actual
names of the input vectors 
For the onesample ztest, the null hypothesis is that the
mean of the population from which x
is drawn is mu
. For the standard
twosample ztests, the null hypothesis is that the population mean for x
less that for y
is mu
.
The alternative hypothesis in each case indicates the direction of divergence of the
population mean for x
(or difference of means for x
and y
) from mu
(i.e., "greater"
, "less"
, "two.sided"
).
The assumption of normality for the underlying distribution or a sufficiently large sample size is required along with the population standard deviation to use Z procedures.
For each of the above tests, an expression for the related
confidence interval (returned component conf.int
) can be obtained in the usual
way by inverting the expression for the test statistic. Note that, as explained
under the description of conf.int
, the confidence interval will be halfinfinite
when alternative is not "two.sided"
; infinity will be represented by Inf
.
Alan T. Arnholt
Kitchens, L.J. (2003). Basic Statistics and Data Analysis. Duxbury.
Hogg, R. V. and Craig, A. T. (1970). Introduction to Mathematical Statistics, 3rd ed. Toronto, Canada: Macmillan.
Mood, A. M., Graybill, F. A. and Boes, D. C. (1974). Introduction to the Theory of Statistics, 3rd ed. New York: McGrawHill.
Snedecor, G. W. and Cochran, W. G. (1980). Statistical Methods, 7th ed. Ames, Iowa: Iowa State University Press.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25  x < rnorm(12)
z.test(x,sigma.x=1)
# Twosided onesample ztest where the assumed value for
# sigma.x is one. The null hypothesis is that the population
# mean for 'x' is zero. The alternative hypothesis states
# that it is either greater or less than zero. A confidence
# interval for the population mean will be computed.
x < c(7.8, 6.6, 6.5, 7.4, 7.3, 7., 6.4, 7.1, 6.7, 7.6, 6.8)
y < c(4.5, 5.4, 6.1, 6.1, 5.4, 5., 4.1, 5.5)
z.test(x, sigma.x=0.5, y, sigma.y=0.5, mu=2)
# Twosided standard twosample ztest where both sigma.x
# and sigma.y are both assumed to equal 0.5. The null hypothesis
# is that the population mean for 'x' less that for 'y' is 2.
# The alternative hypothesis is that this difference is not 2.
# A confidence interval for the true difference will be computed.
z.test(x, sigma.x=0.5, y, sigma.y=0.5, conf.level=0.90)
# Twosided standard twosample ztest where both sigma.x and
# sigma.y are both assumed to equal 0.5. The null hypothesis
# is that the population mean for 'x' less that for 'y' is zero.
# The alternative hypothesis is that this difference is not
# zero. A 90% confidence interval for the true difference will
# be computed.
rm(x, y)

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