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Topic Wise Essay

2310 words - 10 pages

One-Sample Tests of

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.


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
This is denoted by the Greek
letter β.

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
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.


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


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.”


Part of

Larger (or more) than



Smaller (or less)



No more than


At least


Has increased



Is there difference?


Has not changed



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

See left



Conduct a test of hypothesis about a population mean.

Hypothesis Setups for
Testing a Mean ()


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

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

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.

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.


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

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