08 - Hypothesis Testing With z Tests

8/13/2019 08 - Hypothesis Testing With z Tests

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WITH Z TESTS

Arlo Clark-Foos


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Review: Standardization

compares with all other scores (or a population).


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CDC Exam le: Jessica

For 15 year old girls, = 63.8, = 2.66

( )98.0

66.2

)8.6341.66(=

=

=

Xz


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shorter than Jessica?

50% + 33.65% = 83.65%


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than Jessica? 50% - 33.65% OR 100% - 83.65% = 16.35%


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from the mean as Jessica (tall or short)? 16.35 % + 16.35% = 32.7%


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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%


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CDC Exam le: Manuel

Negative z, below mean: 50% - 46.56% = 3.44%


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CDC Exam le: Manuel

100% - 3.44% = 96.56 %


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CDC Exam le: Manuel

3.44% + 3.44% = 6.88%


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Percenta es to z Scores

= =

You find out you are at 63rd percentile

.

X

= .33(100) + 500 = 533


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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


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UMD & GRE Exam le

34.1436.10===

Mz

Consultz table forz = 1.34 40.99 %

. = .


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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


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Assum tions of H othesis Testin


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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).


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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.


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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


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.

H0: 1 2

1 1 2

H0: 1 = 2

H1: 1 2


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.

distribution. Po ulation: = 156.5 = 14.6

Sample: M = 156.11, N = 97

482.16.14===

M


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.

In Behavioral Sciences, we use p = .05

= =

50% - 2.5% = 47.5%

Consult z table for 47.5%z = 1.96


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.

( ) 26.0)5.15611.156( =

=

=MM

z

.M

6. a e a ec s on


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Increasin Sam le Size

value of the test statistic, thus increasing probabilityof finding a significant effect


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Population: = 554, = 99 = =

99 === .90N

34.1436.10

)554568(=

=

=M

z


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Population: = 554, = 99 = =

99 === .200N

00.200.7

)554568(=

=

=M

z

08 - Hypothesis Testing With z Tests

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