Types of Hypothesis Tests

What are you testing?What are you comparing? To what are you comparing? How many?…

Ho: = #One Sample--

Mean

Ho: 1 = 2

Two Sample--Means

Ho: = #One Sample--

Proportion

Ho: 1 = 2

Two Sample--Proportions

One Sample Z for Mean

One-Sample Mean Z Test for X

One-Sample Mean Z Test for

x

z

n

xz

X

One Sample t for Mean

One-Sample Mean t Test for

With n-1 degrees of freedom

nsx

tX

Matched Pair t Test for Difference of Means

Matched Pair (Means Difference) t Test for difference of 2 samples

with (ndiff – 1) df

diff

diff

diffdiff

ns

xt 0

Two Sample t Test for Independent Samples

Unpooled (assuming distributions have different variances)

Two-Sample Means t Test (unpooled/separate) with df

Pooled (assuming both distributions have same variance)

Two-Sample Means t Test (pooled) with (n1 + n2 – 2) df

2

22

1

21

2121

n

s

n

s

xxt

21

2

2121

11

nns

xxt

p

Proportions

One-Sample Z Proportion Test for

Two-Sample Z Proportion Test

n

pz

p

1

ˆ

ˆ

21

21

21

21 ˆ...,11

ˆ1ˆ

ˆˆ

nn

xxpwhere

nnpp

ppz c

cc

How to test?

1) Read problem/situation.

2) Determine Ho and Ha.

3) Enter information/data into computer.

4) Read computer output (p-value).

5) Interpret results in the context of the problem/situation.

Example

Suppose a political candidate has decided to support legalization of gambling if he is convinced that more than 2/3 of U.S. adults approve of gambling.

USA Today reported the results of a Gallop poll in which 1523 adults were asked if they approved of casino gambling. The number who approved was 1035. Does the sample provide convincing evidence that more than 2/3 approve?

Ho: = 2/3 and Ha: > 2/3

1401.08.1

1523667.1667.

667.680.

1523

1035ˆ

ZPZPpP

P-value

ExampleThe Associated Press reported that a management consultant

believes that, on average, workers spend 75 min/day making personal use of company technology. Suppose that the CEO of a large corporation wanted to determine whether the average amount of time spent in personal use of company technology for her employees was greater than the reported 75 minutes. Ten employees were surveyed and data entered into computer.

Ho: = 75 vs. Ha: > 75

T-Test of the MeanVariable n Mean StDev SEMean t pTime 10 74.8 9.45 2.89 -.07 0.53

What conclusion should be made?

Example

Tennis elbow: An article reported the force on the hand just after impact on a one-handed backhand drive for advanced and intermediate players. Is there evidence that the mean force for advanced players is greater than for intermediate?

Adv ( n = 6, = 40.3, s = 11.3) Int ( n = 8, = 21.4, s = 8.3)

Ho: A = I vs. Ha: A > I

x x

004.46.3

83.8

63.11

04.213.409.18

22

tPtPxxP IA

ExampleDES, a nonsteroidal estrogen, was used to treat mothers until

1971 when it was banned due to its link to cervical cancer.

Ten sets of brothers had their spatial thinking ability tested, where upon one brother was not exposed to the drug while in his mother’s womb and the other brother was exposed.

SAMPLE: n = 10, exposed mean = 12.6,

unexposed mean = 13.8

sample mean difference= -1.2, standard error of difference= .5

Ho: diff = 0 vs. Ha: diff < 0

02.4.25.

02.12.1

tPtPxP diff