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# Topic Wise Essay

2310 words - 10 pages

One-Sample Tests of
Hypothesis

LEARNING OBJECTIVES
1 Define a hypothesis.
2 Explain the five-step hypothesis-testing procedure.
3 Define Type I and Type II errors.
4 Define the term test statistic and explain how it is used.
5 Distinguish between a one-tailed and a two-tailed hypothesis.
6 Conduct a test of hypothesis about a population mean.
7 Compute and interpret a p-value.
8 Conduct a test of hypothesis about a population proportion.

10-2

Define a hypothesis.
Explain the five-step hypothesis-testing procedure.

Hypothesis and Hypothesis Testing
HYPOTHESIS A statement about the value of a population parameter
developed for the purpose of testing.
HYPOTHESIS ...view middle of the document...

This is denoted by the Greek
letter .
Also known as the significance
level of a test.

Type II Error

Defined as the probability of
failing to reject the null
hypothesis when it is actually
false.
This is denoted by the Greek
letter β.
10-6

Define the term test statistics and explain how it is used.

Test Statistic versus Critical Value
TEST STATISTIC A value, determined from sample
information, used to determine whether to reject the null
hypothesis.
Example: z, t, F, 2
CRITICAL VALUE The dividing point between the region
where the null hypothesis is rejected and the region where it
is not rejected.

10-7

Distinguish between a one-tailed and two-tailed hypothesis.

One-tailed vs. Two-tailed Test
One-tailed or Left-tailed Test

Two-tailed or Non-directional Test

One-tailed or Right-tailed Test

10-8

How to Set Up a Claim as Hypothesis

In actual practice, the status
quo is set up as H0.
“Boastful” claim is set up as
H1 (we apply the Missouri
rule – “show me”).
Look for keywords and
convert them into symbols.
Some keywords include:
“improved, better than, as
effective as, different from,
has changed, etc.”

Keywords

Inequality
Part of
Symbol

Larger (or more) than

>

H1

Smaller (or less)

<

H1

No more than

H0

At least

H0

Has increased

>

H1

Is there difference?

H1

Has not changed

=

H0

Has “improved,” “is
better than,” “is more
effective”

See left
text

H1

10-9

Conduct a test of hypothesis about a population mean.

Hypothesis Setups for
Testing a Mean ()

10-10

Testing for a Population Mean with a
Known Population Standard Deviation — Example
Jamestown Steel Company
manufactures and assembles
desks and other office
equipment. The weekly
production of the Model A325
desk at the Fredonia Plant
follows the normal probability
distribution with a mean of 200
and a standard deviation of 16.
Recently, new production
methods have been introduced
and new employees hired. The
VP of manufacturing would like
to investigate whether there
has been a change in the weekly
production of the Model A325
desk.

A sample from last year’s weekly
production yielded a mean number
of desks produced of 203.5. Test
using 0.01 significance level.
10-11

Testing for a Population Mean with a
Known Population Standard Deviation – Example
Step 1: State the null hypothesis and the alternate hypothesis.

H0:  = 200
H1:  ≠ 200

(note: keyword in the problem “has changed”)
Step 2: Select the level of significance.
α = 0.01 as stated in the problem.
Step 3: Select the test statistic.
Use z-distribution since σ is known.
10-12

Testing for a Population Mean with a
Known Population Standard Deviation – Example

Step 3: Select the test statistic.
Use z-distribution since σ is known.

10-13

Testing for a Population Mean with a
Known Population Standard...

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