Figure 6.3, page 161. ztail and zdemo are available from ATS and can be downloaded over the Internet using the search command (see How can I use the search command to search for programs and get additional help? for more information about using search).
zdemo 1.5 -1.5
ztail .1336 2
Z-score, page 163; figure 6.4, page 164. zcalc is available from ATS and can be downloaded over the Internet using the search command (see How can I use the search command to search for programs and get additional help? for more information about using search).
zcalc 4.032 4 1.257 627
z-score for sample means
(m - mu) (4.032 - 4) (4.032 - 4)
z = ---------- = ---------------- = ----------------- = 0.64
s/sqrt(n) 1.257/sqrt(627) 0.0502
ztail .5222 2
Z-score, page 164. zcalc is available from ATS and can be downloaded over the Internet using the search command (see How can I use the search command to search for programs and get additional help? for more information about using search).
zcalc 4.032 4 1.257 6270
z-score for sample means
(m - mu) (4.032 - 4) (4.032 - 4)
z = ---------- = ---------------- = ----------------- = 2.02
s/sqrt(n) 1.257/sqrt(6270) 0.0159
Confidence interval, page 165.
cii 627 4.032 1.257
Variable | Obs Mean Std. Err. [95% Conf. Interval]
-------------+-------------------------------------------------------------
| 627 4.032 .0501997 3.93342 4.13058
Z-score, page 166.
zcalc 3.01 0 7.309 29
z-score for sample means
(m - mu) (3.01 - 0) (3.01 - 0)
z = ---------- = ---------------- = ----------------- = 2.22
s/sqrt(n) 7.309/sqrt(29) 1.3572
Test for a single proportion, page 170; confidence interval, page 171.
prtesti 1227 .482 .5
One-sample test of proportion x: Number of obs = 1227
------------------------------------------------------------------------------
Variable | Mean Std. Err. z P>|z| [95% Conf. Interval]
---------+--------------------------------------------------------------------
x | .482 .0142648 33.7894 0.0000 .4540415 .5099585
------------------------------------------------------------------------------
Ho: proportion(x) = .5
Ha: x < .5 Ha: x ~= .5 Ha: x > .5
z = -1.261 z = -1.261 z = -1.261
P < z = 0.1036 P > |z| = 0.2073 P > z = 0.8964
cii 1227 .482
-- Binomial Exact --
Variable | Obs Mean Std. Err. [95% Conf. Interval]
-------------+-------------------------------------------------------------
| 1227 .4816626 .0142645 .4533704 .5100448
Z-score, page 178.
zcalc 4.17 4 1.39 2879
z-score for sample means
(m - mu) (4.17 - 4) (4.17 - 4)
z = ---------- = ---------------- = ----------------- = 6.56
s/sqrt(n) 1.39/sqrt(2879) 0.0259
Confidence interval using t, page 184.
cii 29 3.01 7.31
Variable | Obs Mean Std. Err. [95% Conf. Interval]
-------------+-------------------------------------------------------------
| 29 3.01 1.357433 .2294247 5.790575
Single-sample t-test, page 185.
ttesti 29 3.01 7.31 0
One-sample t test
------------------------------------------------------------------------------
| Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
x | 29 3.01 1.357433 7.31 .2294247 5.790575
------------------------------------------------------------------------------
Degrees of freedom: 28
Ho: mean(x) = 0
Ha: mean < 0 Ha: mean ~= 0 Ha: mean > 0
t = 2.2174 t = 2.2174 t = 2.2174
P < t = 0.9826 P > |t| = 0.0349 P > t = 0.0174
Power of a test, page 195. Stata uses the t-distribution rather than the z-distribution so the results below will differ slightly for the book value.
sampsi 0 10, alpha(.05) sd(18) n(36) onesample onesided
Estimated power for one-sample comparison of mean
to hypothesized value
Test Ho: m = 0, where m is the mean in the population
Assumptions:
alpha = 0.0500 (one-sided)
alternative m = 10
sd = 18
sample size n = 36
Estimated power:
power = 0.9543