08 - Hypothesis Testing With z Tests
-
Upload
halleyworld -
Category
Documents
-
view
224 -
download
0
Transcript of 08 - Hypothesis Testing With z Tests
-
8/13/2019 08 - Hypothesis Testing With z Tests
1/25
WITH Z TESTS
Arlo Clark-Foos
-
8/13/2019 08 - Hypothesis Testing With z Tests
2/25
Review: Standardization
compares with all other scores (or a population).
-
8/13/2019 08 - Hypothesis Testing With z Tests
3/25
CDC Exam le: Jessica
For 15 year old girls, = 63.8, = 2.66
( )98.0
66.2
)8.6341.66(=
=
=
Xz
-
8/13/2019 08 - Hypothesis Testing With z Tests
4/25
CDC Exam le: Jessica
shorter than Jessica?
50% + 33.65% = 83.65%
-
8/13/2019 08 - Hypothesis Testing With z Tests
5/25
CDC Exam le: Jessica
than Jessica? 50% - 33.65% OR 100% - 83.65% = 16.35%
-
8/13/2019 08 - Hypothesis Testing With z Tests
6/25
CDC Exam le: Jessica
from the mean as Jessica (tall or short)? 16.35 % + 16.35% = 32.7%
-
8/13/2019 08 - Hypothesis Testing With z Tests
7/25
CDC Exam le: Manuel
For 15 year old boys, = 67, = 3.19
( )82.1
19.3
)672.61(=
=
=
Xz
Consult z table for 1.82 46.56%
-
8/13/2019 08 - Hypothesis Testing With z Tests
8/25
CDC Exam le: Manuel
Negative z, below mean: 50% - 46.56% = 3.44%
-
8/13/2019 08 - Hypothesis Testing With z Tests
9/25
CDC Exam le: Manuel
100% - 3.44% = 96.56 %
-
8/13/2019 08 - Hypothesis Testing With z Tests
10/25
CDC Exam le: Manuel
3.44% + 3.44% = 6.88%
-
8/13/2019 08 - Hypothesis Testing With z Tests
11/25
Percenta es to z Scores
= =
You find out you are at 63rd percentile
.
X
= .33(100) + 500 = 533
-
8/13/2019 08 - Hypothesis Testing With z Tests
12/25
Table and Distribution of Means
are using a sample and need to use standard error.
How do UMD students measure up on the GRE?
= 554, = 99 M = 568, N= 90
M = = 554 436.10
90
99===
NM
-
8/13/2019 08 - Hypothesis Testing With z Tests
13/25
UMD & GRE Exam le
34.1436.10===
Mz
Consultz table forz = 1.34 40.99 %
. = .
-
8/13/2019 08 - Hypothesis Testing With z Tests
14/25
Assum tions of H othesis Testin
.
2. Participants are randomly selected
.
normal
.
accurate results even when the data suggest that the
o ulation mi ht not meet some of the assum tions.
Parametric Tests
Nonparametric Tests
-
8/13/2019 08 - Hypothesis Testing With z Tests
15/25
Assum tions of H othesis Testin
-
8/13/2019 08 - Hypothesis Testing With z Tests
16/25
Testin H otheses 6 Ste s
.
inferential test, and assumptions
.
3. Determine characteristics of the comparison
Whether this is the whole population or a control
group, we need to find the mean and some measure
of spread (variability).
-
8/13/2019 08 - Hypothesis Testing With z Tests
17/25
Testin H otheses 6 Ste s
.
How extreme must our data be to reject the null?
will reject the null hypothesis (cutoffs)
p levels (): Probabilities used to determine the critical value
5. Calculate test statistic (e.g., z statistic)
6. Make a decision
Statistically Significant: Instructs us to reject the null
hypothesis because the pattern in the data differs from
what we would expect by chance alone.
-
8/13/2019 08 - Hypothesis Testing With z Tests
18/25
The z Test: An Exam le
= = = =
1. Populations, distributions, and assumptions
1. All students at UMD who have taken the test (not just our
sample)
2. All students nationwide who have taken the test
Distribution: Sample distribution of means
Test & Assumptions:z test1. Data are interval
. ,
3. Sample size > 30, therefore distribution is normal
-
8/13/2019 08 - Hypothesis Testing With z Tests
19/25
The z Test: An Exam le
.
H0: 1 2
1 1 2
H0: 1 = 2
H1: 1 2
-
8/13/2019 08 - Hypothesis Testing With z Tests
20/25
The z Test: An Exam le
.
distribution. Po ulation: = 156.5 = 14.6
Sample: M = 156.11, N = 97
482.16.14===
M
-
8/13/2019 08 - Hypothesis Testing With z Tests
21/25
The z Test: An Exam le
.
In Behavioral Sciences, we use p = .05
= =
50% - 2.5% = 47.5%
Consult z table for 47.5%z = 1.96
-
8/13/2019 08 - Hypothesis Testing With z Tests
22/25
The z Test: An Exam le
.
( ) 26.0)5.15611.156( =
=
=MM
z
.M
6. a e a ec s on
-
8/13/2019 08 - Hypothesis Testing With z Tests
23/25
Increasin Sam le Size
value of the test statistic, thus increasing probabilityof finding a significant effect
-
8/13/2019 08 - Hypothesis Testing With z Tests
24/25
Increasin Sam le Size
Population: = 554, = 99 = =
99 === .90N
34.1436.10
)554568(=
=
=M
z
-
8/13/2019 08 - Hypothesis Testing With z Tests
25/25
Increasin Sam le Size
Population: = 554, = 99 = =
99 === .200N
00.200.7
)554568(=
=
=M
z