give you an error message if you put in a decimal for x or n. For example if
p
ˆ
= .22 and n = 124 then .22*124 =
27.28, so use x = 27.
Note: the calculator does not have a confidence interval for a standard deviation or variance
Chapter 8
Hypothesis testing for one sample
x Hypothesis test for one sample population mean when V is known, test statistic is
n
X
Z
0
V
P
.
Press the [STAT] key, arrow over to the [TESTS] menu, arrow down to the [1:Z-Test] option and
press the [ENTER] key. Arrow over to the [Stats] menu and press the [ENTER] key. Then type in
the hypothesized mean (
0
P
), sample or population standard deviation, sample mean, sample size, arrow over to the z,
<, > sign that is the same as the problems alternative hypothesis statement then press the [ENTER] key, arrow down to
[Calculate] and press the [ENTER] key. The calculator returns the z-test statistic and p-value.
x Hypothesis test for one sample population mean when V is unknown, test statistic is
n
s
X
t
0
P
. Press the [STAT]
key and then the [EDIT] function, enter the data into list one. Press the [STAT] key, arrow over to
the [TESTS] menu, arrow down to the [2:T -Test] option and press the [ENTER] key. Arrow over
to the [Stats] menu and press the [ENTER] key. Then type in the hypothesized mean (
0
P
),
sample or population standard deviation, sample mean, sample size, arrow over to the z, <, > sign
that is the same as the problems alternative hypothesis statement then press the [ENTER] key,
arrow down to [Calculate] and press the [ENTER] key. The calculator returns the t-test statistic
and p-value.
Or (If you have raw data in list one) Arrow over to the [Data] menu and press the [ENTER] key.
Then type in the hypothesized mean (
0
P
),
1
L
, leave Freq:1 alone, arrow over to the z, <, > sign
that is the same in the problems alternative hypothesis statement then press the [ENTER]key,
arrow down to [Calculate] and press the [ENTER] key. The calculator returns the t-test statistic
and the p-value.
x Hypothesis test for one sample population proportion, test statistic is
¸
¹
·
¨
©
§
n
qp
pp
Z
00
0
ˆ
. Press the [STAT] key, arrow
over to the [TESTS] menu, arrow down to the option [5:1-PropZTest] and press the [ENTER] key. Type in the
hypothesized proportion (
0
p
), X, sample size, arrow over to the z, <, > sign that is the same in the problems
alternative hypothesis statement then press the [ENTER] key, arrow down to [Calculate] and press the [ENTER] key.
The calculator returns the z-test statistic and the p-value. Note: sometimes you are not given the x value but a
percentage instead. To find the x to use in the calculator, multiply
p
ˆ
by the sample size and round off to the nearest
integer. The calculator will give you an error message if you put in a decimal for x or n. For example if
p
ˆ
= .22 and n
= 124 then .22*124 = 27.28, so use x = 27.
Chapter 9
9.1 Confidence Interval and Hypothesis Test for Two Population Means Large Independent Samples
x Hypothesis test for the difference between the means of two populations
21
PP
, independent samples, σ
1
and σ
2
known, test statistic is
¸
¸
¹
·
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
2
2
2
1
2
1
21
21
nn
XX
z
VV
PP
. Press the [STAT] key, arrow over to the [TESTS] menu, arrow
down to the option [3:2-SampZTest] and press the [ENTER] key. Arrow over to the [Stats] menu and press the
[ENTER] key. Then type in the sample or population standard deviations, the first sample mean and sample size, then
the second sample mean and sample size, arrow over to the z, <, > sign that is the same in the problems alternative
hypothesis statement then press the [ENTER]key, arrow down to [Calculate] and press the [ENTER] key. The
calculator returns the test statistic z and the p-value.
x The 100(1 - D)% confidence interval for the difference between the means of two populations
21
PP
, independent
samples, σ
1
and σ
2
known is
2
2
2
1
2
1
2/
2
1
nn
zXX
a
VV
r
. Press the [STAT] key, arrow over to the [TESTS]
menu, arrow down to the option [9:2-SampZInt] and press the [ENTER] key. Arrow over to the [Stats] menu and press
the [ENTER] key. Then type in the sample or population standard deviations, the first sample mean and sample size,
then the second sample mean and sample size, then enter the confidence level. Arrow down to [Calculate] and press
the [ENTER] key. The calculator returns the confidence interval.
9.2 Confidence Interval and Hypothesis Test for Two Population Means Small Independent Samples
x Hypothesis test for the difference between the means of two populations
21
PP
, independent samples, σ
1
and σ
2
unknown. The test statistic for unequal variances is
¸
¸
¹
·
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
2
2
2
1
2
1
21
21
n
S
n
S
XX
t
PP
. Press the [STAT] key, arrow over to
the [TESTS] menu, arrow down to the option [4:2-SampTTest] and press the [ENTER] key. Arrow over to the [Stats]
menu and press the [Enter] key. Enter the means, standard deviations, sample sizes, confidence level. Then arrow over
to the not equal, <, > sign that is the same in the problems alternative hypothesis statement then press the [ENTER]
key. Highlight the No option under Pooled for unequal variances. Arrow down to [Calculate] and press the [ENTER]
key. The calculator returns the test statistic and the p-value. On the TI-83 press the [STAT] key and then the [EDIT]
function, enter the data into list one for males and list two for females. Press the [STAT] key, arrow over to the
[TESTS] menu, arrow down to the option [4:2-SampTTest] and press the [ENTER] key. Arrow over to the [Data]
menu and press the [ENTER] key. The defaults are List1:
1
L
, List2:
2
L
, Freq1:1, Freq2:1. If these are set different
arrow down and use [2
nd
] [1] to get
1
L
and [2
nd
] [2] to get
2
L
. Then arrow over to the not equal, <, > sign that is the
same in the problems alternative hypothesis statement then press the [ENTER] key. Highlight the No option under
Pooled for unequal variances. Arrow down to [Calculate] and press the [ENTER] key. The calculator returns the test
statistic t and the p-value. (note: the regular 8
th
edition textbook has a different df rule, calculator returns
¸
¸
¸
¹
·
¨
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
11
2
2
1
2
2
2
2
2
1
2
1
2
2
2
1
2
1
nn
df
n
s
n
s
n
s
n
s
.)
x The 100(1 - D)% confidence interval for the difference between the means of two populations
21
PP
, independent
samples, σ
1
and σ
2
unknown for unequal variances is
2
2
2
1
2
1
2/
2
1
n
s
n
s
tXX
a
r
. Press the [STAT] key, arrow over
to the [TESTS] menu, arrow down to the option [0:2-SampTInt] and press the [ENTER] key. Arrow
over to the [Stats] menu and press the [Enter] key. Enter the means, standard deviations, sample
sizes, confidence level. Highlight the No option under Pooled for unequal variances. Arrow down to
[Calculate] and press the [ENTER] key. The calculator returns the confidence interval.
Or (If you have raw data in list one and list two) press the [STAT] key and then the [EDIT] function,
type the data into list one for sample one and list two for sample two. Press the [STAT] key, arrow
over to the [TESTS] menu, arrow down to the option [0:2-SampTInt] and press the [ENTER] key.
Arrow over to the [Data] menu and press the [ENTER] key. The defaults are List1:
1
L
, List2:
2
L
, Freq1:1, Freq2:1.
If these are set different, arrow down and use [2
nd
] [1] to get
1
L
and [2
nd
] [2] to get
2
L
. Then type in the confidence
level. Highlight the No option under Pooled for unequal variances. Arrow down to [Calculate] and press the [ENTER]
Learning Center 1875 SW Park Avenue, Millar Library, Portland, OR 97201 503.725.4448 www.pdx.edu/tutoring
TI-83, TI-83 Plus or TI-84 for Non-Business Statistics